If you are flying close to the ground, turn downwind and have an engine failure, disaster is certainly closer than if you have that same engine failure into the wind.
However, the helicopter doesn't know (or care) whether it is flying with 75KT airspeed and 50KT groundspeed or 75KT AS and 100KT GS. Once you are in the mass of air, it doesn't matter at all if the air is moving or which direction it's going, until you have to touch the ground. Turns, climbs, OGE hover - doesn't matter whether the wind is 330/18 or 00000, as long as you aren't trying to hold station to a point on the ground.
For a light helicopter, even a gust of wind doesn't change performance much (as long as you are not attempting to maintain a consistant ground speed), as the aircraft will just be accelerated by the wind. Not so for a loaded 747-400 - the inertia of that aircraft will mean that a wind gust causes a significant change in airspeed and resulting performance.
We're so used to flying helicopters by referring to points on ground that we sometimes forget that the air doesn't care. Swimming across a placid river is no different than swimming across a lake unless you are trying to hit an exact spot on the opposite shore.