My experience is to leave bee trees that have fallen any distance. 90% have collapsed comb and dead queens and it becomes a salvage operation, don't mess with it unless you're getting paid. If you can be there and see the trunk/limb get lowered down by all means take it home. I'll still do those kind of rescues for free.
If a bee tree has been laying on it's side for more than 24 hrs and the bees are still there the queen is dead.
That is a sad fact to learn. I know a logger and asked him if he ever downed bee trees. He said occasionally it happens if the hive was not detected before cutting. Loggers don't want hollow trees.
So I am guessing that most hives with a still living queen abscond ASAP after the tree goes down? Doesn't it take her a few days to trim down enough to fly?
Next odd question. If the hive was in a portion of the tree that was left in the woods - like the tree top. Would the smell of old comb attract future swarms if the top is still slightly propped up?