It's an interesting question. The technical answer is "no", because it has been stated here that each and every event is independent of any event in the past. Essentially, the PB game essentially states that given enough PA's, across all permutations of leagues & makeups, that a .300 hitter will hit .300 in PB.

The truth is that I don't exactly know what "mysterious" things in the algorithms actually effect PB performance. I know, for instance, that I have a certain "average" player in Brad Ausmus who batted .275 last season and .266 this season (MLB). He has NEVER spent any considerable time (in PB) over the Mendoza line over the entire season and a half, ending last season around .205 and presently at a sweet .199 through 115 games this season. He is a highly rated catcher, but I'm starting to think that he will NEVER play up to par for my team, or even close. I play in a pretty average ballpark, so there's not a lot of reason to think that has much to do with it, either.
The mathematics of the situation state that he should be a better hitter, but the question begs : are there things in the game that would cause certain combinations of players/ballparks/whatever to perform in a "skewed" manner as compared to the numbers ?

Based on everything that they tell us, the answer is that players should approach their "real" capabilities as we increase the sample-size (the favorite catch-phrase of this bulliten board). That would tell us that a player should be rated on his statistics, not his PB performance.

Either that, or they have snuck in the "Kenny Rogers" algorithm, so that certain players can't perform in certain cities !!!