The appearance of singers seems to be a topic of confusion amongst people. I've decided to write out a full, complete response to this kind of a question.
Do looks matter? Does it matter what you look like? Do you have to be pretty to be a singer?
The answer: It depends. What type of singer do you want to be?
If you want to be a pop star - one that everyone obsesses over for a few years and claims is going to be super important in the history of songs, only to disappear completely after several years - then yes. Looks do matter. If you want to be the next Miley Cyrus, Selena Gomez, Demi Lovato,...