As with prior responses to your questions, it’s all about what is in your contract. So I’m theory you can get time off to do this but then it becomes about how much, how your compensation is structured etc. if you’re private practice you need partners that are agreeable to covering your patients and having you be missing from the call schedule. They might do that for a couple weeks but it gets harder when you are talking about extended trips. If you are hospital employed they are not going to want to cover your salary while you are gone. I have a friend doing rural general surgery in the northeast and had it in her contract that she got 3 months every year to dedicate to global health/mission trips as that is her passion. Then a new administration took over and when she went to try to schedule this contract-guaranteed time for the first time after 18 months or so they told her at the most she could go for 2 weeks and accused her of “hiding” this clause in the contract (which if you knew her, she definitely didn’t as she is far from being a legal ninja). She ended up quitting over it for breach of contract.
So yeah, you can do some of this as a surgeon but you’ll likely only be able to do short stints and you’ll have to use vacation time to do it.
