Gotcha. I don't know if USAF
crews would just reel the basket in. My guess is they'd just take the thing off and just strap it on a pallet. Maybe have an MRT come out for the problem which caused the drogue to stay trailed if there was no hydro specialist on the flight already. Long answer yes with an "if", short answer no with a "but".
I'm not sure what you mean by cutting the hydraulics, but your last part was right. When you land with the boom in trail it's not as if the boom is rigid and won't move around at all. It'll go wherever the slipstream (and ground) make it go. Don't think it will break off, all I've heard is the boom just scrapes on the ground like you'd expect.
If anyone knows where I can post a 22 MB
video file of a KC
-10 landing in Alaska (Elemendorf) with the boom in trail I'll post the thing. Still waiting for the Fairchild B-52 to be digitized though