I think you may be able to do some of this without a ton of work - my recollection is that ProfileOAuth2TokenServiceFactory is the factory that creates a platform-specific ProfileOAuth2TokenService, which is the service that stores and generates OAuth2 tokens for the signed-in account. You'll want to build a version of Chromium that uses the desktop version of ProfileOAuth2TokenService instead of the Android version.
The big thing you'll probably be missing is the signin UI itself - not sure if some of those classes are missing on Android or not. You won't easily be able to hardcode your username and password, because we try pretty hard these days to drive people through a web flow for password entry (for various security and product reasons) - not even sure if it's possible to generate an OAuth2 refresh token from a raw username/password any more without going through a web flow.