the issue with dropping an airliner from height is by the time it gains enough airspeed, it no longer has control authority to pull out. Airliners are not really designed to go through a dive like that and come out in one piece.
Glide restarts of engines are possible (if not core locked) but it also isn't something done very often.
As long as it doesn't end up in a flatspin an airliner should be able to pull up from a dive. For an extreme example where this was tested in practice, in the https://en.m.wikipedia.org/wiki/China_Airlines_Flight_006 incident, a pilot lost control of a 747 & ended up diving 30k feet at speeds approaching/potentially exceeding mach 1, then pulled 5 Gs leveling off at 10k feet once he regained situational awareness, & they were still able to land safely, although there was some damage
IMO the bigger problem would be needing multiple helicopters pulling together - wind or the jet's engines might pull the helicopters enough that they'd crash into each other, & you'd definitely want to start the engines before freefall..
Glide restarts of engines are possible (if not core locked) but it also isn't something done very often.