One interesting thing to me is that I don't think fletched arrows are as affected by a crosswind as, say, a bare shaft. What I have observed is that the fletches act almost like a rudder on a boat and help keep the arrow moving in the direction it was shot.
This is the way I think it works: the wind blows the fletch end of the arrow sideways more than the point end, so the arrow goes downrange at an angle. But as it's going downrange, the air it's passing through is also exerting a force trying to straighten it out, but it can't, because of the crosswind, and the combination of the two forces actually helps keep the arrow on course, albeit at an angle.
A crosswind will move the POI in the direction the wind is blowing for any arrow, fletched or unfletched. But I don't think it has as much of an effect on a fletched arrow as it would on an unfletched arrow. At least, I've noticed that when I shoot in a crosswind strong enough to make the arrow fly downrange at an angle, I still hit pretty close to the mark I was aiming at. Of course, when the crosswind gets strong enough to blow the arrow off the shelf, then all bets are off.