For people who really value their personal time and space, this could be a rough transition. Andover is often intense, for both adults and students, as there is a great speed in the culture. For instance, my 2nd year, I lived in a large boys dorm and it was tricky to balance what I needed and what the kids needed at different times. In some ways, just by virtue of being on campus, you are always mentally 'on', even if not working. Some manage to maintain their own boundaries for their time, and that I think is key if you want to work at boarding schools in the long run.
For those looking to apply as early career teachers, it can feel a bit isolating at times if you're from farther away. It's likely a bit easier if you're from the MA/NH area already.
For people interested in teaching, you learn a lot, but very much by doing and getting help from those around you. It's not equivalent to things like the Penn Program where you earn a M.A. while teaching and doing other programs.
I don't regret the experience at all though. It's a great place to learn a lot about teaching and schools as a whole with people who care a lot, but it is very much an elite perspective, for what it's worth.