At some level it probably does. Even in Rocket League, which is more cosmetic than most, if your teammates are passing to you more than they would have with the default skin, then you'll do better.

As a medic in team fortress 2, I usually pocket and ubercharge the players with cosmetics. It's an important team resource, and the odds of someone with a "default" skin making good use of it are fairly low. Much like plumage for a bird it's a reliable signal of "virility" - if you're invested enough in the game to own a $200 hat and a coordinated outfit then you've probably played it long enough for me to trust you sight-unseen.

http://i49.photobucket.com/albums/f278/katietiedrich/comic26...

If you're a pro player with the default skin, you're gonna have a bad fucking time, because you're last priority for heals, you're not getting an ubercharge, etc. That is gameplay-affecting even if the cosmetic itself is not.