Yes, I think confidence plays a bigger role than we think. Few years ago, I had full head of hair, but had weak game and confidence when it came to girls. I had girls that were interested in me, and were making "first step" towards me, but they certainly weren't the "hottest" girls in my eyes. In the best, they were average or slightly above average. Hottest girls very rarely make a first move on a man, even when they are attracted to him.
So, when I was trying to pick up the hottest girls, I basically failed, because I didn't know how to talk and act properly, and I think they felt I was not confident. So most of the time, they ended being taken away from me by guys actually uglier than me (i.e shorter, ugly face, worse posture, and most important - sometimes with even less hair!), but I saw that they had one advantage above me - that was the confidence. I saw that they were more relaxed than me when talking and approaching a girl, they knew how to treat a girl properly.
I consider myself attractive (wow, what an immodesty), I mean I got everything - the height, good face, good posture etc. Of course now I have less hair, but then I would say I was "flawless", and I could compete with most guys, when it came to looks.
In the recent years, I learned how to muuuch better lead the game with women, and I became much more confident. And it makes big difference. I actually suceeded with some of the hotter girls, despite my hair loss (I'm currently NW2, but with bad diffusion on top). I learned how to treat girls, and I feel when they feel comfortable with me. I know how to create "spark" between us, when the atmosphere becomes sexually tense. Everything matters when you approach the girl - appropiate conversation, appropiate posture, appropiate touching of a girl.
So that said - confidence matters A LOT!