Not alone, no. But there's a strong correlation between population size and economic strength, and econimic strength is one very big source of importance.
While I agree economic engines will have Nobility(as others said , the OTU has a built in mandate of 1 noble per world, that noble can be either Marquis(Marchoness) or lesser(in OTU view) Baron(ess). Your comments suggest you're not a fan of that.
But I would say that the more important noble positions, beyond regional capitals, are where flexability is needed. This is rare in an economically powerful area as many resources can be brought to bear. That's why I have so much interest in Risek. Considering only economics is 1 sided, ignoring command/control and strategy. Your view is admittedly valid but, IMO, flat. I believe(and I may be wrong) ignores regions where economys have fallen or never risen. These areas need flexible, dynamic and (hopefully) charismatic/pursuasive figures to lead populations that may be demoralized or even rebellious. So the right nobility and the right strength of Rank may be key to growing or even maitaining the peace there. You can't just rely on the Imperial Navy as Gun point will eventually lead to a rebellion.
A population level of 5 means that the number has five zeros following the initial digit,...
You are correct there and , as stated, I was working from memory while at work. Mistakes will be made.
I haven't analysed the astrography of the region, but a casual examination would seem to indicate that the naval bases at Inthe and Aramis are more likely to be the staging areas for defense of respectively Regina and Aramis.
Actually, what happened in the FFW makes me think as I do. From a Zho PoV the invadsion was two pronged(The Spinward Marches Campaign). Rimward(South) fleets hit the Mirriam, Frenzy and Denotam Systems (Vilis subsector) while bypassed by the "Hammer"(40th fleet) for Rhylanor some penetration battles and resupply at the "secret base". Coreward(North) fleets hit and sieged the Efate and Regina Systems allowing huge amounts of material to be tied up rather than blockading the systems and driving deeper to destroy the Imperial defenses or preventing significant counter strikes.
That suggests that a better Rimward fleets strategy could have placed the front lines at(if not past) Inthe(Regina Subsector). Imperial planning, especially as commented on in the early JTAS TAS News articles, would have recognized this likelyhood and planned for a support base behind the likely front lines so their main supply and staging worlds would not be over run in the initial wave(s) of an invasion.
As for the Vargr question(s), the fleets were not slow but glutonous. They moved in quickly and largely took primary targets well enough. What happened after, the looting and general break down of control of the "fleets" is what halted them. The result of sudden changes in wealth or status in any significant Vargr hierarchy, while not expressly written by GDW, are obvious and you can only choose to ignore them. Squadron leaders will find themselves challenged by a ship captain or two after they pwehaps led their section's part in a strike or that captain faced down a significant threat as "fleet on fleet" degraded to tactical. The sudden shift as a captain becomes locally famous or gains the ability to offer great wealth is the collapse of the fleet structure from within. If you ask what evidence there is, look to the means used by the Zhodani to get the Vargr to join in. The removal of Imperial power in the region would have meant an "Expansion reward" to an organized Vargr government yet they did not join in the invasion. The fleets that did join in were large masses of corsair bands, nothing more. As fot the other question. I feel I was misread or the OTU misinterpreted. When you say:
There's not a shred of evidence to suggest that there would be enough threat from Vargr forces to Deneb Sector that the subsector fleets wouldn't be more than enough to contain them.
You fail to recognize that there is also not a shred of evidence that there are not significant Vargr forces present. And in both cases, you would be correct considering purely CT sources. However in MT, the main thrust of Vargr invasions come from teh Deneb and Corridor sectors! Now, I agree...this is CT we are talking about. But because an author ends one book and then starts a new book does not mean they ahve not written the over all storyline and broken that up into books. So I feel comfortable in assuming that GDW's intent was to have large organizations of Vargr building up and collapsing regularly but providing for a constant pressure against Imperial expansion coreward as well as a large threat against raiding and/or local invasions. I admit that is an assumption based on the documentation of the OTU, but it is no more valid than your assumptions.
So I assume that initial Imperial responses would have been slowed both by the speed of communications as well as the need to make sure that there would not be strikes further riftward(east) either to affect the lines of supply or as targets of opportunity vs even the local coursair bands that would have seen a drop in the defenses of Deneb Sector systems as reinforcements were forwarded.
So I have no secret cache of information, I am just unwilling to assume, based on the largest scale map of the known universe and the vase size of the Vargr extents, that the only point of friction or military hazard is the Spinward Marches. No Admiral pulls a majority of forces from a region assuming that "these guys" are not tied to "those guys" simply because "these guys" may choose to attack simply because half my guys left to fight "those guys". I hope I put that plainly enough as I was trying to convey a fairly complex statement simply.
The shipyard facilities of Risek are described in BtC as high-quality, but small. That's another thing that's correlated to population size: shipyard size. Even if the facilities on Risek are 100 times bigger than the average for its population, they would still be smaller than the yards at Inthe.
And, as someone else pointed out in this thread, even slightly damaged ships take up 100% of their space in repair docks. As such, I can repair a great many smaller ships at Risek while forwarding the larger ships to larger repair facilities. This is the most efficent way to repair the most ships the fastest. As well, this supports the creation of "near the front" skirmisher squadrons" as the larger ships are repaired and form up with smaller support reinforcements forwarded from Rhylanor into CruRons and BatRons. They can then either move forward and integrate with the skirmisher squadron formations or build a stronger "Defense in Strength" as the skirmisher's are forced back.
So the question finally comes to why Risek? Or even, why does it have a naval base anyway?
My answer, which need not be your answer, is based on the assumptions of the Admiralty BEFORE the FFW. The Zho's have always had Vargr support so it will either be organized or disorganized. If it is disorganized it holds little threat and that front can be commanded from Aramis. But if the Vargr fleets are organized and well commanded, then the front "Will Be" Aramis. you can say, 'but it did not happen that way' but the Imperial Admiralty obviously thought it might...or why pay to have a base at Risek in the first place??
Add tot hat the assumption that a heavy Zho thrust would not drive towards Rhylanor(because that was what they did last time and no one makes the same mistake twice) but choose to crush the Regina and Vliis Subsectors. So Inthe(Regina) would become the main front line base. As a result, you need a base that will do three thigns for you:
1) Support Inthe(or Regina if you are very lucky)
2) Support Aramis
3) support strikes coreward into the scattered handful of low tech and disconnected systems that offer a web of stepping stones between Regina's well defined clusters and the Towers cluster. Striking up through that space will allow a savvy Admiral the ability to take slightly longer jumping smaller ships to places from which they can conduct "hit and run" ops against the enemy's flanks(Aramis Front), Rimward line(Regina Front) or even drive into Vargr space to hit supply lines.
Finally, the Foreven question.
The chief forces of Sword world Might was directed against The Darrian, not The Imperium. As such, the Darrian were not a major force against Zhodani attack from Foreven Sector. As well, through the TAS News Feeds GDW made it clear that worlds like Trexalon(a Zho Client State) made the most of the war embarking on a shadow war of Privateering vs Collace. Between the sudden availability of prizes to the independant worlds in that subsector, the ongoing Trexalon/Collace shadow war and the activity of the normal pirates and other hazards to merchant operations(as District 268 was Far from Secure by GDW's own documentation), The Imperium would have many needs to feed from Glisten(who's fleets were also documented in the Sinward Marches Campaign as having been tasked with standing guard against further Sword worlds invastions IIRC).
Sorry that this has been long but I felt it should be complete to be proper.
I have t say, I am glad that I posted here because it has forced me to think through things deeper than I had before in many areas and widened out nicely

Thank you to most who responded.
To the one who posted:
"Oh, as far as YTU is concerned, I wouldn't dream of contradicting you."
I am sorry you feel it needed to bring sarcasim to this debate and hope I only mis-read it that way. I can see both the OTU and MTU much better for 99% of what has been said here.
Marc