is it at all reasonable that someone of humble origins who has already entered the Nobles Career could advance to high levels within that career and exit the career still of humble means afterward as the NORM, not the exception.
I can not respond to this specifically until you explain further the phrase "humble means".
In regards to Soc characteristic, I think it entirely possible. The norm... my thoughts vary. I think a typical dilettante could move up from wastrel to Ingrate, Black Sheep and Scoundrel without any increase in Social standing. An administrator, still not much of an issue; int, and edu and skills in admin and such may very well be more important than social standing for this nobility career specialization.
As I've mentioned before, I think putting those three specializations together under the title Nobility is the biggest issue. The following is the only one that really seams to fit.
Diplomat.... here we might have an issue but if we consider that the low soc character getting qualified for diplomat is statistically rare and not the norm and moving up through the ranks is statistically difficult with a -DM, then it is not a common thing to have a low SOC high rank diplomat. If somehow the dice fall that way, so be it.
If one hands out free SOC you now make it more common for the low SOC character that somehow gets into the career to gain soc and continue moving up in ranks. Is that the "norm" for people who somehow manage to get a assistant or intern position to all be quite good and capable and earn soc so they keep advancing? I'm not saying that one could not house rule some such. It makes some sense for the diplomat specialty to have higher ranks have SOC rank benefits like navy captains and admirals.
There are those that believe the hard line SOC = position. For those with this view I understand and see how some Nobility career specialties and tables are an issue. I think of all the possible diplomats throughout the imperium though. Does the ambassador of one country to another on some TL8 world have the same SOC as an imperial ambassador of one world to another, as the imperial ambassador of one sub sector to another, as the imperial ambassador to the Aslan... I'd just consider a low SOC ambassador to be one of the smaller fish. In a possibly structured and ranked society, the SOC 14 character is destined to rule and would likely never be a clerk or 3rd secretary of some country on some TL8 world. They would intern within a suitably high soc organization.
I feel that if a DM is applicable, perhaps due to a characters rank in a certain career, then the GM should apply it. There are examples in the rules for navy ranks giving DMs, why not do so for diplomat ranks? In some cases, the skills the person gains as they progress in their careers could help explain how they moved up and how they are capable of doing their jobs An admin task uses that possibly low SOC skill but the character has gained a bit of admin skill over their career and thus gets by.
As regards the OTU: The Imperium has historically rewarded men and women of ability and initiative, and often does so through advances in Social Standing
As I've pointed out before, the OTU Imperium seams a military based governmental structure. Folks that do take initiative and show leadership gain social status while the administrator or diplomat doing a great job pushing papers behind a desk is less likely to be rewarded.