1. It is possible to calendar / drive / plus account without gmail. just use your non-gmail account to create them.
2. I wanted to do the same, ie. to add my google calendar to iOS calendar app but failed. The app assumes that there will be a gmail account, attempts to connect to it but fails. It bombs out and returns to the Account screen.
I tried to kill the app while it is attempting to connect to gmail but fails.
Workaround #1. If you only want to view the calendar events but not create new event against that calendar, you can share it had have the iOS calendar app subscribe to the shared calendar.
Workaround #2. Not something that I prefer but you can use another calendar app instead of the built in iOS calendar.
Any proper solution?
[UPDATE: Solution found - use CalDAV]
[behaviour observed in iOS 10.3.x]