Wouldn't winning the war require the import of similar troop numbers anyway? Often, troop numbers are reduced during occupation.
No and especially no if the 3I has a tech advantage and dominates close orbit. To win a war requires achieving set objectives, for example destroying the war fighting capabilities of the En. This will take less resources the greater the tech disparity. Every time the En concentrates their forces, your high tech forces get to move in and destroy them supported by ortillery.
To provide the newly "liberated" population with the sense of safety to carry on their daily activities, enjoy public infrastructure and start thinking about governance, you need a lot of sophonts on the ground talking with and protecting the population. Some of which will/may come from existing local police/paramilitary & military forces.
I can picture an Imperial TL15 Division cleaning up a TL10 Army 20 times its size quite comfortably. Come the "peace" tho' you only have enough troops to guard the seat of government, the space port and some public infrastructure. The population will feel you are "hiding" in your fortified zones, coming out only for raids. The cities will be hot beds of insurrection and resentment and the hills will belong to the freedom fighters. Your 10-12,000 troops have no chance of winning over a high pop world.
Equally we haven't had anyone bombing our infrastructure and playing us off against each other. Hmmm...Omelettes and eggs.
Perhaps you are confusing a 200 year plan vs a 20 year plan.
200 years is a very long time. Long enough for Earth to progress from TL4 to TL7 and Pop8 to Pop9 without outside assistance. (And assistance is there for the asking, all you have to do is trade nicely...)
And if, by any chance, 200 years isn't enough - double it.
At what point does the cost of interdiction exceed the cost and taxation profits of invasion. 200 years, 400 years, maybe 50 years?
ooo... you would make a great evil dictatator! lol. That might work, will have to think that one through. Offering off world scholorships might do it without the Dr Evil connotations. Hmmm, where has it been done b4? I'm thinking the Romans had a version...There is one way you might do it in a generation or two (and it's been done before) with ratios around 1:100 or so - take all the children into an Imperial enclave at age 2 and release them back into the community as well-adjusted Imperial Citizens at age 20.