Yes. Power split will affect the target after the user switches out. The effect on the target only disappears when the target switches out. (so the user's stats will also stay the same if the target switches)
I know this because I battled myself.
Turn one shuckle uses power split on hydreigon.
Turn two Shuckle switches to gengar and hydreigon's dark pulse does not OHKO (does around 70%).
I tried the same thing again but without using power split, and dark pulse OHKOes every time.
So power split's effect must have persisted after the user switched out.