While I admit I haven't tried, it should be possible to run an Android phone without ever signing into Google - indeed without a Google account whatsoever. The email application support POP, IMAP or Exchange, the contacts can be synced with SyncML or Exchange (and a few other options I am sure), applications can be sideloaded, IM+ does a pretty good job with Jabber etc. Surely it would make it somewhat more complicated but I am quite sure it is possible.
In other words - Google offer a way for people to run the smart phone without any knowledge about servers and with an extremely simple setup (enter your google account once), but it is in no way forced upon you - so I think it's actually quite acceptable.