ORIGINAL: Washington Hunter
If you're shooting a drop-away it shouldn't matter, no.
This is not always true. I have a Trophy Taker Shakey Hunter and I have to have my cock vane down and to the left. This makes it so one of the vanes is pointing straight up. If I were to shoot them any other way the vanes would hit my rest. The feathers may not be affected by the rest though, buthaving the feathers hit the rest wouldn't do anything good for the arrows flight.