They won't regurge just because they're in shed. If you feed live you may want to wait until he's not shedding or check same-day return policies if you don't want to be stuck with a rodent, but if you feed f/t there's no reason not to offer food to figure out whether or not he'll eat during shed.

I have some snakes that don't act any different during shed, and some that turn into nervous wrecks and won't even look at food. Just depends.