I do think so, but what youll most likely see is that it hugely differs per world. In Gunheads a Lt Gen was mentioned to have fought as a tank commander himself, though it is hard to extract a clear conclusion I think it is safe to say that it does happen.
If you take the Cadia, its a world(or a group of worlds?) that is fully militarized, so I do think infantry, IF they would survive long enough (IF IF IF) could be promoted to a staff function, though what you mostly see is, fm the books ive read, is that guar get promoted for showing bravery and heroisme in the face of the enemy.
But, to be fair, a guardsmans live is practicly worth less then his gun - shows how ruthless the 40k universe is. Most will die, but some will be promoted.
I also think with the Valhallan regiments that there is a certain aristocracy that often holds the higher ranks, but i cant remember exactly.
Great book btw is Fifteen Hours, really short but powerfull story - shows exactly how expendable a guardsman is.