Although every web mail provider is different, you implied that your webmail is powered by Google. If that is the case, then it uses the same base technology as every other e-mail service powered by Google. So that would mean that, unless your ISP's implementation of Google mail was extremely nonstandard, most likely your experience would be similar to any other webmail powered by Google.
My work e-mail is powered by Google, and it works fine on my iOS devices. I don't use Android, but since Android is itself made by Google, obviously Google webmail works just fine with Android.
If you did indeed mean that your e-mail service is powered by Google, and if you were correct in stating this, then I think there is about a 99% chance it will work correctly. Of course, I can't make any absolute guarantees because I'm not familiar with your specific provider.