That might make a difference in real life where emotions can contribute to momentum. But I do not think it matters much for strat where it is strictly a numbers game. Everyone always cites the instance of what happens if the road team splits the first 2 games and then wins 2 of 3.
But wait. What about when the home team wins those first 2 games?
But really when I have home field advantage I do not really care. All I really ask is get through those first 5 games and get me back home and I will take my chances. I should have set up and planned it out where I have the matchup advantages those last 2 games. And I feel if I am the better team and in theory I should be if you were the wild card I can often win 2 of 3 on the road.
But I will concede the point. Next time you are leading a division let me see if you tank games down the stretch to get out of the lead and contend for the wild card. That will tell how much you really believe the wild card has the advantage.