Yes.
In the massive ONE YEAR of having a 12-team playoff (thus posing the question of "what happens to the loser of the conference championship game"), there has NEVER BEEN (in one year) a conference championship participant SO CLOSE TO THE CUTLINE as we have with Alabama and BYU.
I just wish people could be honest about this fact, instead of bloviating (with no support) about how Alabama will "never be left out".
The commissioner that was removed said this before he was removed and stepped down at Baylor:
“We look at it as a positive if you’re playing in the championship game. It’s another datapoint. It’s certainly recognized when we think about record strength,” Rhoades said. “Obviously, you win it, that’s a plus. If you lose it, theoretically, it’s not supposed to hurt you.”
The key word is theoretically, as Rhoades laid out.
“If it was a game where it wasn’t competitive and you completely got blown away, then that would be a conversation, candidly, in the room amongst the committee,” he added.
So you're right, its possible. They've opened the door this year. Last year they had the stance of "absolutely not" until it came to the possibility of it happening to the ACC. They said it could impact the seed but they won't fall out of the picture if they were "in" while other teams sit idle.
Quote from the chair in 2024:
"If you take, for example, Tennessee is ahead of [ACC title game participant] SMU, Indiana is behind SMU; Tennessee will not drop below Indiana at any point. Neither team is playing,” Manuel said. “But SMU could move up, depending on how we evaluate the game. They could stay where they are or they could move down depending on the outcome of the game. But Tennessee and Indiana in this example would never flip. Indiana would never move ahead of Tennessee, and Tennessee would never drop below Indiana because we’ve already evaluated them. There’s not another datapoint because they’re not playing in the championship games. So we don’t have anything else to add to the evaluation of those teams, so we can’t move them above or below each other.”
From another article: CFP Selection Committee Chair Warde Manuel said last week that teams would not be penalized for losing conference title games and leapfrogged by teams that were idle Saturday.
In the same discussion he said - "“Potentially, yes,” Manuel said when asked directly if SMU could drop below Alabama on Sunday. “And they can move above teams, as well. Again, it just depends on the outcome of the game.”
So he talked out of both sides of his mouth. It'll take a blowout of BYU and/or Alabama for them to fall out.