All parachutes need plenty of height to deploy: very few people have survived a bail-out under 2000 ft. That said, a whole-vehicle recovery system should work from a lower height because it is designed to lower the aircraft with the people still inside, so there's no bail-out needed and the only predeployment activities are to realise there's a serious problem and to pull the red knob.
However, even the rocket-extracted Ballistic Recovery System isn't guaranteed to give a safe recovery from less than 400 ft in straight and level flight or from less than 1000ft if the aircraft is spinning. Almost any other imaginable circumstance is likely to have a safe recovery height within that height range, though there doesn't seem to be much, if any, data on how well a BRS system would deploy after engine failure in a hovering aircraft which would still be falling relatively slowly.
But, IIRC all the above minimum survival height estimates assume deployment is over flat ground, so no allowance is made for the incident occurring over trees, tall buildings etc. or the possibility of the aircraft colliding with something while the chute is deploying and the plane still has significant forward speed.