Their app is still running all the time. I do not know what exactly it is collecting, but I'm sure it sends a lot of information to Google. Even just the fact that Google knows my IP (which is otherwise dynamically assigned) at any time is too much.

On the other hand, if you try selectively enabling and disabling the service, the push notifications stop working. LineageOS + MicroG is a much better solution if you only need them occasionally and if you prefer an app which does not actively (try to) spy on you.