Blood Pact said:
Their main obligation is that they produce massive amounts of war material for the Imperial war machine, through the byzantine quasi-fuedal system that is setup throughout. And aside from that, they're largely free to do what they want.
This is how I see it as well.
I still go by the old IG Codex fluff which detailed how a regiment is raised exactly, and the text basically had fresh troops make a "detour" to the next Forge World in order to take on additional vehicles, heavy weapons and other assorted equipment not sponsored by their own homeworld, and only after this would the transport proceed to the staging area and its cargo's actual destination.
However, OP, this is not to say that it absolutely has to be this way. 40k background is very inconsistend and conflicted when it comes to details such as these, and you are just as free to deviate from established norms as any official writer. All that matters is how you and your players would think about the end result, so perhaps make it dependent on your group's reaction?
Aside from simply ignoring some fluff, one could also try to find a compromise. ranoncles already mentioned one option on how you could pull this off.
For another, how about you have a Forge World that was originally conquered and occupied by the Imperial Guard and only later turned over to the AdMech, who quickly proceeded to erect gigantic manufactorium and habitats, importing large masses of labour to speed up construction? The soldiers that once settled the planet remained as a garrison and integrated into the local populace - at first seconded to the Mechanicus for maintaining law and order, then simply forgotten. In other words, the regiment was never officially disbanded. Fast forward a couple centuries and some clerk finds a datatome which contains the regiment's battle record and the Adeptus Munitorum files a request to the Mechanicus to return the regiment to them. Needless to say, all the original soldiers are long dead, their battlegear having become lost, traded, recycled or heirlooms. Still, on paper and by Imperial law, the Munitorum has the right of it - and so the Adeptus Mechanicus proceeds to re-establish the regiment. For added lulz, they might even attempt to track down the grand-grandchildren of the original garrison to conscript them for military service. Sounds just wacky enough to fit right into the nightmare bureaucracy of 40k, no?