It's fine if that's what you expose by default, but you really do need to give the user a checkbox or something so they can input their own if they have one. I have an OpenID I use everywhere, if I come to one of your sites and end up using my google ID instead it will cause me nothing but frustration and end up being less secure.
In fact I'd probably not login to your site because of this if I didn't have a compelling reason to do so.