Yes, it does. Which is why it should NOT be at neutral site. The team with the best record should get home field advantage due to the fact that they already beat the team they'll have to play in the championship game.
From a thread last May taken from an ESPN article:
To mitigate the risk of having a 2-loss team beat an undefeated and knock both out of the CFP and help protect the Big 12’s top playoff contender, I have another suggestion.
Instead of going back to playing the conference title game at a neutral site,
the Big 12 should hold it on the home field of the regular-season champ.
This would boost the conference in four ways.
- It would give the Big 12 that 13th game the playoff committee holds so dear.
- It would offer the Big 12 regular-season winner an opportunity for another quality win.
- It would diminish the chances that the Big 12 champ would lose.
- It would provide the Big 12 with a whole lot of national buzz, something the league has lacked in the post-realignment era.
Imagine Texas traveling to Norman for the first time in almost a century, or Oklahoma running through the tunnel at Darrell K Royal–Texas Memorial Stadium.