In my experience, it IS possible to resupply damaged HQs. However, this only works up to a point, after which further resupply attempts have no effect and you have to wait on the trains.
It takes 2 hours for auto-repair to fix a fully dead HQ. Thus, it should take 1.5hrs for auto-repair to fix a damaged HQ that's lost 3 of the 4 functions. However, if you get 4 or 5 guys to do multiple supply runs each, the HQ will be back to normal in 20 minutes or so. So obviously player resupply helps damaged HQs. Reports to the contrary seem to be wrong.
There comes a point, however, when player resupply seems to lose its effectiveness even though the HQ is still damaged. As this point is approached, the perk awards per supply run start to decrease from 3.something to 2.something to 1.something and finally become 0. When this happens, the HQ will still be lacking the nme dar function.
However, resupply still seems to work for part of the time the nme dar function is down. For instance, tonight Rook HQ was short only the nme dar function. Me and a couple of others ran supply runs and got perks for a while, then we all got 0, and the nme dar function stayed down the whole time. It took the arrival of a train to finish fixing HQ.
Anyway, that's what it looks like to me. There are definitely still bugs in HQ resupply, but it's nowhere near as bad as it once was. IMHO, resupplying a damaged HQ is effective, especially if the HQ has lost 2 or 3 functions. But once it's lost only 1, resupply soon quits working.