Simple answer - No.
The fact is Thor has no dog in the fight when it comes to Civil War. He has more to worry about anyway, and his secret identity hasn’t been used for years, and even then wasn’t really the same thing.
Avengers start fighting each other then sure there is a reasonable argument that he wouldn’t pick sides, but that is partly proven wrong by Secret Empire, where being guided by his trust of Captain America and Mjölnir placed him on the wrong side and then his uncertainty made him question Cap and change sides.
To be the ‘heart’ of the team one needs to be partly moral guide, partly the one everyone is close to, partly the one who cares about everyone, partly the one that holds the idea of the team above their own place in it. Even the biggest Thor fan couldn’t make the claim Thor ticks all those boxes.