No, not from JavaScript. Once you're on the server side, you can contact the mail server and see if it rejects mail to that address, but that's not 100% reliable either, because many mail servers (qmail and MS Exchange in particular) don't check existence of recipients during the SMTP exchange.

If the address entered belongs to the guy who enters it, it might be warranted to send a confirmation mail, just as this forum does. Again, though, that's server-side stuff.