Here's the problem with that theory. You're XYZ Sports Network and you just paid a gazzilion dollars for the right to televise the CFB playoffs. The most loved/hated/watched college football team in the country goes 12-0 against a respectable schedule, and you are going to accept that they are ineligible for the playoffs you just paid all that money for? Part of the value of the playoffs lies in their legitimacy in crowning a champion. You make a rule whereby a team that clearly shows itself to be in the top 4, or top 8, or top whatever, cannot be in that playoff, you now lose legitimacy, you lose value, and the network paying all the money will not accept that. And fair minded CFB fans won't either.
I don't know if college football will require it to be a conference champion but I can see where they could especially if 64 to 72 teams break away to form a new division. The requirement to be in the new division of 64, might be contingent on being in one of the 4 conferences that a lot of people would assume would be left.
Even until then, I can see where even if the CFP doesn't state teams are eliminated if not in a conference and a conference champion they may require a ND be undefeated or a better record than the other conference champs. Who knows maybe they would even take a 11-2 Michigan who was a conference champ over a 11-1 ND.
In theory ND may be eligible but in practice when they go into the room to make the decision most of the selection has an allegiance to a conference. ND does not have that affiliation and I wouldn't be surprised if they find themselves squeezed out of the playoffs in a lot of situations.