The Angels reportedly just signed a new TV deal worth $3B over 20 years. I'd guess that it's backloaded to some degree, so let's say for the sake of argument it starts at $131M in 2012 and goes up $2M/year after that.
Say you had a 40,000-seat stadium and hosted 81 home games per year. You charge $70/ticket on 10% of your seats, $60/ticket on 10% of your seats, $50/ticket on 20% of your seats, $30/ticket on 30% of your seats, $20/ticket on 20% of your seats, and $10 on 10% of your seats. If you sell out all 81 games at those prices, you'd make $120M.
Angels ticket prices are probably a little higher than that, but but we can see that roughly speaking, this puts their local TV revenue on the same magnitude as what we might expect their ticket revenue to be. On top of that, they've got national TV revenue from the league, luxury box sales, parking revenue, concessions revenue, and ad revenue from the outfield walls, etc. I don't really know what those add to the bottom line, but it's not hard for me to envision a total revenue of about $700-800M next year.
How much extra money can signing Pujols make them in the really short term? I don't think it's too bit a stretch to say that adding Pujols, not so much adding any kind of star appeal there is, but adding 6 wins next year, pushes them close to 48K/game attendance next year. It doesn't seem like a huge bump from 40K/game, given the size of their market. Then say they get revenue from an additional 3 playoff home games (1 in ALDS and 2 in ALCS), at ticket prices double that of regular season games, because Pujols (or Pujols/Wilson if you want to look at it that way) is enough to push them ahead of the Rangers. That'd be roughly an extra $24M in regular season ticket revenue and an extra $10-11M in postseason ticket revenue.
So in the short term, it's pretty easy to see outcomes where the Pujols signing turns a profit for the Angels. In the longer term, I think the security of that long-term TV deal gives the Angels enough payroll to compete even if Pujols is nearly a non-contributor, and by that point they've potentially gained a bunch of fans along the way.