I don't think so. You can only have one Div2 school every so many years, I think, or only one Div 1aa (or whatever it is called now, FBS). But I don't think it has to be P5, just FCS.
As things stand now I think an SEC champion would probably have to have 3 losses to not make the playoff. It might be easy to engineer a scenario on paper where a two loss champion wouldn’t make it but it’s unlikely to happen.
P5 is a conference rule since we only play 8 conference games to shut up the other conferences as well as the rivalry games schools. FBS games count annually now. You can count one a season to bowl eligibility.
Didn't know that about the SEC rule of P5. Good rule, really, as it gives the patrons of your school return for the money you invest. Who wants to see 4 sister of the poor schools?