After the lip that DD1 (13) gave me yesterday, yes I would, in a heartbeat! 
Seriously though, if it was what any of our children wanted, then DH and I would allow them to attend.
DH and I both attended a boarding school from the age of 13, in fact it's where we met, and first started dating at the tender age of 14. However, even without that, I had the most amazing time, and DH did too. This was in the early-to-mid 90's, and even back then, boarding school was nothing like it once was. People still believe it's 'dumping your kids there and leaving them to it', but parents are expected to be engaged, and be in regular contact with their children. I know that those in charge of pastoral care at our old school, would soon be contacting parents to raise concerns, if they felt the parent wasn't being as involved as they should.
DS1 (15) was offered a boarding place at mine and DH's old school, but his final choice was to attend as a day pupil at a school close to home, which is also a boarding school. He attended the junior (pre-prep/prep) part of this school, so ultimately he chose to continue at the same school. DD1 made that same choice.