Mysterui brought up how the "Pujols Effect" on hitters batting directly in front of him might be a fallacy, so I dug into Baseball-Reference and mined some data to see if I could come up with some conclusions based strictly on hitter performance.
An objective analysis of the Pujols Effect would also look at pitch selection thrown to those hitters, but I'm not sure you're going to be able to get that data, and even if you are, it's going to have a ton of noise related to it because you'd have to account for each pitcher's repertoire, how often they generally throw each pitch, how often they throw strikes, and then determine whether there's a significant change in how they pitch when Pujols is in the on-deck circle. This would be something for VEP or someone with a database of pitches from Pitch F/X to try and tackle if they could come up with a query that would search out that type of stuff. It's way above my head, so you'll just have to settle for my quick and easy method here.
Here are the Cardinals 2nd hitters' sOPS+/tOPS+ since Pujols started hitting 3rd on a regular basis in May of 2003 (sOPS measures the difference between the teams' hitter in that spot and the league average hitter in that spot. 100 would be equal to league average, > 100 would be better than average, etc., just like OPS+ normally distributes, tOPS+ measures how much better a better did in this spot in the order)
Year tOPS+/sOPS+ Player Games Hitting Second
2009: 94/92 Rasmus (74), Ryan (21), Ankiel (15)
2008: 120/132 Miles (34), Ludwick (30), Duncan (17)
2007: 133/128 Duncan (45), Ankiel (36), Taguchi (26)
2006: 99/98 Duncan (54), Taguchi (32), J-Rod (22)
2005: 96/103 Walker (44), Edmonds (34), Nunez (26)
2004: 105/117 Renteria (53), Walker (34), Lankford (30)
2003: 94/104 Drew (46), Edmonds (34)
Again, what were looking at is whether these guys performed better in the 2nd spot than they did elsewhere in the lineup (the first number) and how that spot in the lineup did compared to the league average 2nd spot for all teams combined, including the Cardinals (sOPS+, the second number). Considering Tony likes to bat power hitters in the 2nd spot and other managers don't, I would expect the sOPS+ to be above 100 most of the time for the Cardinals, and that's pretty evident here I think, so we probably should handicap the sOPS+ just a tad, adding 3-5 points or so as a WAG. I could look back historically with LaRussa, but that would take a lot of time, and it's Friday, and I'm blowing off a bunch of work I need to get done to do this anyway, so you'll just have to make this assumption with me.
As far as I'm concerned that's a pretty neutral distribution, because the two strong years are carried by guys who happened to have career years that season (Duncan/Ankiel in '07, Ludwick in '08) never to see similar numbers like that again, it just happened to be that they hit in front of Albert. It's really, really hard to state that those guys wouldn't have hit well elsewhere in the lineup had they been batting there. The numbers below 100 feature a lot of Jim Edmonds, who hated batting second (regardless of who was batting third) and voiced that opinion numerous times as I recall. Also, 2006 and 2009 would probably look very similar if it wasn't for Duncan's breakout late in the season.
Conclusion: It's not much of an advantage to be batting in front of Pujols, at least in the macro sense.
FWIW, the most successful guys seems to have hefty splits (Duncan killed RHP, terrible against LHP; Ludwick destroys RHP, not good against LHP; Taguchi destroys LHP, terrible against RHP; Ankiel destroys RHP in '06, struggles with LHP; etc.) TLR seems to like to put platoon guys there, whether that says something about the "Effect" I have no idea.