Cross Eye Dominance

[MW]

I would think some of the answer would be predicated on what style of aim the person is trying to employ.  If instinctive it shouldn't matter. If it is truly like throwing a ball there are many pitchers whos dominate eye does not match their throwing arm but they can throw with accuracy.  Any other where you are "lining up" two points it may have a greater impact.

Just my two cents...

[Pat B]

When shooting instinctively eye dominance doesn't matter. Just look where the arrow will go(the spot), draw and release. Your brain will do the rest if you have practiced enough. In normal hunting range knowing the distance doesn't matter either.

[TSHOOTER]

[YosemiteSam]

My wife and my oldest son are RH with left eye dominance.  They both shoot left handed.  Gapping is an easier way to learn to shoot but that only works when you're using the correct sight picture.

Echoing McDave, at some point, archers can benefit from learning how to shoot with both hands.  It's fun and a good challenge.