In the United States, how customary is it for professors to not check their emails around Christmas?
Yes, it's common. Many take a break from work entirely during this season. Some reduce their working hours to spend time with family, and only answer urgent email. Some may be traveling and have limited or no access to email. Some (like me) may be swamped with grading and other end-of-semester duties and are focusing on those at the moment.

If you haven't heard back by mid-January, try a polite follow-up then.