I'm not a fan-boy of Google stuff. Good old Google has been hit in the past with various tools, methods that allowed people to get to personal data that they should not have been able to. At least on my Domain it's attack surface and presence is quite minimal and is a LOT less likely to have some generic user stealing data.
Google is just too darn good at storing, sorting, data - just not as good at keeping it under wraps from non-authorized people all the time.

Not sure what your needs are Sue for mail and if it has to do with public access BBS then probably not that much of a privacy concern anyways.