How about implementing Google Plus login API? It's not really setting up a full OAuth process since G+ it's fairly simpler, even if it is actually built on top of OAuth.
I use that in an app I'm developing that also does not require online access (except for initial G+ login access).
What I do is the first time the app is run I present the G+ login button. After user clicks on it he can accept the permissions request from my app (to be able to retrieve user email and some basic profile info, i.e. minimum permission needed) and if the API client connects correctly then I present the user with the dashboard or home screen and also set up a flag in SharedPreferences about the user being already authorized.
In this way, the next time the user starts the app it will remember it was already authorized and just ask the API client to connect (only if the access was revoked from the account's Play Store website do we need to re-verify that the user auth is still valid), and everything should work. If the user revokes the access to his G+ profile from my app, I clear the flag so the next time the user runs it it asks for authorization again.
It's actually very simple and at least for my use case (Which sounds very similar to yours) it works for what I want it with minimum user intrusion.
I strongly suggest you try out something like this Google Plus login tutorial
Edit: You can also check this question I asked before, about working with multiple activities that need Google Plus functionality
Also, forgot to say that with this method you are always sure that the user account is always valid since you are checking directly with Google's servers about its validity.