I think there is a misconception that students at Yale (and other Ivies) experience a lot of pressure. I don't think that's true for most kids--except for the pressure that they exert on themselves. Most of them are super-active people. Yale (at least for the majors I know about) isn't really a cut-throat, competitive environment. People work hard because they are hard workers.
It's not for everybody, certainly, but I think that if a student is accepted, he or she can almost certainly handle it.