If she really wanted to go with him, she could have said "that's okay you don't need a tuxedo for prom." Or "that's okay; my brother has one of those tuxedo tshirts and is about your size."
You're only cooked if you choose the latter option and he says "have fun at prom with your older brother."
What if he's just making up a reason because he doesn't like you at all? If you're weird and pushy he'll tell everyone! It already took weeks of imagining that interaction and mustering the courage to do it.
No, this plan is a bust. It's obvious you're interested; you just asked him out. So if he is too, then he'll just tell you. Obviously.