He does go back stage to change into a t-shirt that isn't soaked with sweat, then reappears (without telling his brothers where the hell he's going, as is customary for him). He's also a perfect gentleman--or, at least, the Andy version of a perfect gentleman, which means that he's friendly and remembers not to make more than three off-colour jokes, and actually keeps his casual misogyny under wraps. He's also very good with fans, and it's safe to say this is probably one of Rachel's best experiences with a very semi-celebrity, especially since as he doesn't want to sleep with her he doesn't do anything creepy or leery at all.
He even, in a fit of generosity brought on mostly because of Daphne's being there, ends up footing the bill.
After which he gives her a brilliant grin and says, "Can I get you away from your mates, then?"