I agree that there is a mental aspect to the game. A-Rod clearly isn't held back by it, or if he is then you should be asking yourself what type of player he would be if he were mentally stable, given that he is on track to become possibly the best player in baseball history.
Hitting is a reaction and a habit. You have 4/10ths of a second to decide what to do. A-Rod is more than capable of using that time effectively, again, evidenced by his past success. For example, If this were the only season we had seen him, it would be VERY easy to decide that David Ortiz is a patently UNclutch performer. In the past few weeks alone I've seen time after time where he doesn't "come through".
In Manny's last 5 playoff series he has hit .300, .412, .300, .385., .310. from the NYY series in 2003 to now. I'm pretty sure he is near the top in playoff HRs, RBIs, etc., in history. Before that, he was pretty bad and known as NOT being clutch. He hit a HR off of Barry Zito in the 5th game (I believe) of the ALDS, and watched it leave the yard, which pissed off the announcers. The reason I remember that is that they had just been talking about what a great hitter he is but how he just couldn't get it done in the clutch of the playoffs. It's BS. Some guys will happen to hit right away in their playoff career and become known as 'clutch', others take a little while to get to their average performance.
Manny has played in a total of 81 playoff games.
A-Rod has played a total of 35 playoff games.
He is more than equipped to hit 4 HR in a playoff game just like he is equiped to do that in a regular season game. The dude is a baller.
Regardless, though, I don't think he's coming to Boston. I think the Sox will use that as a smokescreen while they make a better deal elsewhere. You can't get a player who is better than A-Rod, but with 30 million dollars you could have Roy Oswalt, Josh Beckett and Carlos Beltran. The Yankees will overpay out of fear that the Sox will blow them out of the water again, A-Rod may or may not take it. Personally, I see A-Rod as a Cub, the pride of Mark Cuban's franchise; they will have a chummy relationship.