AFAIK, push notifications require a Google account to work (they piggyback on GTalk), so does that mean for apps for the Kindle Fire are doomed if they use the standard C2DM
You can't use C2DM to Kindle. I don't know why Dule's answer above says he could use Parse to push to Kindle - their service is C2DM and there is no mention of a Kindle client in their docs.
Urban Airship works only because they have their own client, which is fine, but it's not standard.