Planetary governors would defect in droves: "More trade, better FTL transport and communications, better protection than the Imperium can offer in a month of Sundays (can we say 'planetary shields') better medical treatment... where do I sign?"
I'd like to believe this, I'd like to have that much faith in the essential rationality of the human race, but I think the ecclesiarchy, who certainly will be stressing the difference to the common pious folk, and the AdMech whose monopoly and power base are directly threatened, have their claws in too deep- and so many of the Galactic Empire's political class were cartoon characters, some literally but you know what I mean.
We're basically talking about an unquantifiable here anyway, yes? The level of real loyalty/devotional stupidity, delete as appropriate, in the IoM system. Which is certainly going to vary from place to place anyway. I can see a patchwork response, some digging their heels in, some throwing themselves into the arms of the invader, a lot more hedging their bets.
Anyway, even after that, the newly administered military district still has to be protected from counterattack, weeded out of diehards, and those promises have to be made good on. Logistically, it's going to be relatively easy, biggest headache being what to do with this mass of dead, obsolete IoM technology, but psychologically, re-education will be a massive problem. Financially, how long is it likely to take before these conquered territories give a worthwhile return on investment?
What GE agencies actually exist to do all this? if it's COMPNOR and the ISB, who are not really known for their light- handed, masterfully dextrous approach to anything, then that could be counterproductive, breeding rebels and resisters.
To control an area consisting of thirty six full member worlds, and 40,000 settled dependancies.
Yeah, it's not as if 40k's unique in that kind of minimalism.
Also, Calixis is far from typical. Notice how it's choc-a-bloc with Inquisitors?
Chommell sector, though, is atypical; thirty-six member worlds is a very low slice of the supposed million full member states of the Republic- which may be multi- world in themselves, and the forty thousand dependencies all have to be monitored and protected.
I think the force density's different- a hundred and fifty worlds, seventy-five ships, versus forty thousand worlds, four hundred ships (Carrack and larger) because the fundamental tactic is different;
the Imperial Starfleet's biggest threat is rogue elements of itself, logistically speaking it could be a lot larger and the limiting factor on the number of ships is, I think, the number of reliable men available to command them. At that, it still goes wrong sometimes- the fleet still has it's Ozzels and Zaarins.
They can afford to depend on rapid response, having the sensor coverage of their own turf and the speed to go to wherever they're needed.
The Imperial Navy of the IoM has a lot more real enemies, and can't react that fast. They need much higher force density to protect their territory, and at that it still doesn't work too well.
As for the inquisitors, that's the point I'm trying to make. (Militarily they're irrelevant, it's not as if they all brought their own black ships or anything.) Calixis is frontier space, relatively well developed for all that, and it has more than it's share of wierd problems, social kinks and dangerous aliens that the Inquisition are there to deal with.
The morning after the invasion, all those problems drop into the lap of the Imperial military governor.
Bollocks.
Which are precisely what I was trying to cover, by going with the million worlds estimate as a first approximation which the numbers are based off, and mentioning that some people, to wit Connor, think there could be much more of it than that. I think he mentioned "Could be many more, possibly into the billions".
Some of the ships in that sixteen hundred figure for the Imperial sector group are glorified patrol boats; Corellian Corvettes are not ships of force by any stretch, and there are a lot of similar marginals. Until someobody- probably me- goes through the Imperial Sourcebook and works out what ships fit into what formation where, and adds it all up, this isn't going to be any more than a rough estimate, but I reckon that at least a half of the Imperial Starfleet sector group are basically picket boats.
Galactic Empire ships are flat out better in many, many ways- in terms of raw firepower I reckon an Imperator is more or less a battleship, but refined firepower, after working in differences in gun pointing technology, sensors and ECM? The disparity in effectiveness should be very high. This could start to look like quality vs. quantity.
Defections? Yes, there'll be some.
. Between re-building the necrodermis, phase shifting to avoid lightsabre beams (and Force attacks?), and really being a magical energy being (well, sort of 
), a C'Tan is pretty damn hard to kill. There's also the fact that Palpatine may be killed by the necrodermis exploding should he win in combat - remember Khaine's fight against the Nightbringer...