That would be an odd behavior since most users already know that the content of the box is inside the box. I would simply make the box big enough to fit most email addresses.

If you still want to flirt with the idea, I saw this code around and tried it in LF Forms. Works fine, but there might be others more elegant.

Just replace the "youremailbox" with the class name of your email box.

  $('.youremailbox input').keypress(function() {
    var txtWidth = $(this).width();
    var cs = $(this).val().length;

    if(cs>17){
       $(this).width(txtWidth+5);
    }
});