In my opnion, the answer is obviously not. Why he should give himself a lot of headache? and there is also a private issue and security issue if he gives his e-mail.
No, probably not. If I were famous I would make a separate E-mail for fans and go through and read it sometimes just so I know what my fans wanted to say to me. And it'd be funny to read a bunch of crazy girls E-mails! :) (I'm putting myself in his shoes, I wouldn't have crazy girl fans, I'm a girl) :)