I work in a PP group in a medium sized city. Our partners take 14 weeks vacation currently (took 16 last year). It would still be really difficult for anyone to get eight consecutive weeks of vacation. You might be able to randomly string them together in some really unpopular month like october or november, but it'd be pretty hard with the way we pick vacation weeks. It wouldn't be fair for everyone else if someone just said "I want july and august off". My group would never go for it.
Academic groups are a different story, but I still don't think it's gonna be a popular idea. Think how many of your attendings from residency had to fight tooth and nail for a half-day a week of non-clinical time to work on research or talks. Now picture them trying to peace out for two months at a time. Not teaching residents, not producing research, not doing administrative stuff, not producing revenue in the OR.
Basically, the idea of doing mission work/MSF/etc doesn't really line up with the prime directive of either of these types of practices. Honestly, unelss you're in a group of anesthesiologists who all place the same importance on this type of work, you'll likely be screwing your partners/department somehow (time, money, extra work, whatever). Why would they buy into that?
The best idea if you want to do this stuff is work locums. Then no one gives a s%*@ how much time you're off traveling the globe. It's your show, your time.