Some mail clients use an external HTML engine in order to show HTML mails. Thus, showing a form should work. Only when you submit something, problems may arise as mail clients simply aren't built for submitting data. You could try with Javascript & AJAX, but most probably it would fail.
Not yet talking about highly restricted webmail services including gmail and hotmail which both throw out Javascript and probably forms-html too. Also not talking about mobile email clients (all the iPhones and androids of this world), which even more likely won't support it.
As suggested earlier, your best bet is to just mail people a link, as that decreases the problem % with a great bunch.
PS: Obviously, PHP can't run within a mail. But you'ld have submitted it to a external PHP page than