Is it possible to set up an email form (embedded) on the home page that only displays if the user is not opted in to our emails or not recognized?
If the person is not recognized, i.e. the session is not associated at all: Yes, simply use Known Visitor HTML ("If Known Visitor, Show Custom HTML" in Form Editor » Setup).
Did you purchase web personalization? If so, you should be able to do it that way by selecting the div you want to have the form appear in. You could then define the field in your database you want to use to show the form (or whichever content you want).