I always, always, always shoot a drop away, no mater what it is, with the cock fletch up. The only way I could see this being a problem is if you are using very tall fletchings that would contact the crossbar of the QAD. A simple way to see if this is going to be an issue is to slowly pull the arrow through the rest in the upright position. Because you are using feathers, you will not damage them during this little test. Assuming that the cock fletch does not come in contact with the crossbar of the rest, it would be smarter to nock your arrows cock fletch up. This way, you will give the rest more room to get out of the way of your fletchings. Make sense?

I doubt that it would cause the arrow to fly differently.