Can you check your gmail from this phone? Yes, the native email reader supports IMAP and MS Exchange, both of which work with GMail.
Do you mean other Google applications? Not so much. Gravity supports podcasts via Google Reader. PickrUpr allows you to upload photos to PicasaWeb. Other than that, some stuff is available through the web interface.
If you are a heavy Google Apps user, then Android will be your phone OS of choice.