You don't need to use a phone number for iMessage and FaceTime, IIRC it also supports email addresses.
That said I'm in some apple limbo land where I need to switch to an email address for iCloud but it won't let me use mine since I had a pre-email appleID. Yay.
You can't change your "username", but you can set it to send all correspondence, recovery, etc, to your non-gmail address.
Oh well, I avoid logging in anyway :)