I liken it to being a customer of two banks. AGOL is bank 1 and AGE is bank 2. You wouldn't want to cross the streams. AGOL and AGE are separate entities, so logging into one, will not allow you to bounce to the other. That said, OpenID Connect is an option, you can log in to that IDP, and it passes your token to the application you visit. So if you log in via OpenID connect then you can go 'straight into' AGOL, and then 'straight in to' AGE. As long as you follow the links for the OpenID Connect screen.