No, it won't ring on the phone but assuming you allow notifications for the Google Home app and your phone isn't in do not disturb mode you will get a push notification that someone is at the door.
I apologize for my late response and thank you for all of your patience while waiting for a reply. I can definitely understand how frustrating your situation must be, but I wanted to make sure that your issue was addressed. Do you still need help with this issue? I know that there's been a delay in response since you posted.
Please let me know if you need further assistance.