I can't vote because my answer is yes and no. It really depends on what you're exactly talking about. If you're refering to someone who is a musician and literally just plays an instrument for a band, then no.
Honestly, the only people who "have to be beautiful" are pop stars. Then again, only about 10%, if that, of all pop stars are musicians or let alone even write their own songs. If you're going mainstream and wanna be a pop idol, yes; looks and sexiness sells and that's all the mainstream music industry is interested in.
As long as you look good, some corporate lacky will write music that ignorant people will eat up as long as it is "by" a pretty face. Look at Birtney Spears for example. She's cute. That's it. She can't sing. She don't write music. She's just a marketable piece of music-industry ass that will make money. Same goes for Justin Bieber, Rhihanna (or however the hell you spell it), Beoynce... etc.
Now, if your a pop idol that plays a guitar, like countless other over-rated, dime-a-dozen, wannabes out there, yes. You still have to be "pretty". As long as the front man/woman is good to look at, there's a chance you can be pimped out by a record company.
Oh, and no matter how "pretty" your face is, you have to be thin to be "sexy". Name one over-weight pop icon. Didn't think so...
You don't have to be talented to be a pop star. Just look good. Corpoprate musicians will do the rest. As you may have guessed by now, I hold no respect for these "musicians".