I could see it happening without good music. Not that I think the music will be bad, just that it might be the sort we don't notice. And why should music influence believability? The music isn't literally part of the story. What makes a story believable is if the plotline has its own internal logic and the characters behave in ways that are true to their motivations. Music enhances the audience's emotional response, which is entirely distinct from whether the story and characters are plausible.
So far, they seem to be doing the right thing with the casting. Uhura, Chekov and especially Spock. The latest rumors about Sulu and Scotty casting at TrekToday also sound good. So music or no music, I'm still pretty hopeful this will turn out well.