I think if he needs a burp, he won't go deep into sleep, because the gas bubble will be making his tummy hurt. So if he's nursing to sleep, he's fine.
When my son was tiny and still needed burping after each feeding, I wouldn't even sit up in bed to do it. While still lying on my side, I would prop him up against my hip and pat/rub his back to help get the bubble up. Talk about a lazy nurser! LOL. But seriously, when you're exhausted, even these tiny measures can make a world of difference in how much rest you get and how you feel the next morning.