I'm not sure, but I might. They'd be in separate rooms, though. I'm up all hours of the night and when i do sleep, I do so lightly, so I don't think they'd be up to anything right under my nose.
I remember being a 16 year old kid, and if my boyfriend had been allowed to sleep over, I wouldn't have dreamed of doing anything with him with my parents right down the hall.
We'll see if I still feel the same when DD is 16, though.
ETA: I read the question wrong...I wouldn't let my DD spend the night at a boy's house, but I might, just might, let a boy spend the night over here under my eagle eye.