Adding a google account without gmail on iPhone
It is supported. This is what it looks like under settings -> calendar:
Try adding the account as a mail account and then turning off mail and turning on calendars. This is what it looks like in the calendars app:
CalDAV (located under the "Other" account option) is possible, but if you have 2FAC enabled, it's not going to work out of the box. You'll have to create a special application specific password and use that password instead of your regular google password in order to get it to work.