Most of the time, yes, but with the random nature of baseball and somewhat small and scattered sample sizes, once can expect variations from players' norms. Not everyone is going to hit exactly the same as their career norm in clutch situations any more that they would in any randomly picked sample size.
It would be like saying hitting well on Mondays is a repeatable skill.
Now, with all this being said, I do think there may be a slight influence on a player's numbers under the intense pressure of a bases loaded, 2 out situation in the 9th inning. Some players may be able to stay calm and focused more than others, and maybe their personality allows that to be repeatable, but with hitting a baseball being so hard to do, that influence is likely very close to negligible.
You don't make MLB being someone who wilts under pressure.