Zachary Levine, the Houston Chronicle's stat guy, takes a swing at this pitch. And I don't think he misses. He says that Berkman's offensive struggles haven't hurt the Astros the most. Of course, the answer to the question depends on how you measure the amount of damage caused by a player's offense. And Levine uses Fangraph's WPA (Win Probability Added) which measures the extent that a player's offense improved or diminished the team's probability of winning games.
So who has the worst WPA and WPA/LI (based on leverage situations)? Jason Smith is the answer. The surprising part to me is that Jason Smith can amass a -.83 WPA and -.60 WPA/LI in only about 25 at bats. Levine shows the ranking of worst WPA players in the NL and Smith ranks as the 6th worst. But, the telling part is that Smith's 25 at bats, by far, are the fewest at bats to accomplish that amount of damage. For example, Chris Young and Brian Giles accomplished their league worst WPAs in 128 and 137 ABs, respectively. I assume Smith's high rate of damage relative to playing time has something to do with his role as a pinch hitter in key situations. Also, the fact that he has failed to make a positive offensive contribution at any time doesn't help.
The Astros' desire to use a roster spot in this manner is puzzling.