Maybe a little. I started wondering about this when I saw that their AVG with runners in scoring position was .340 while it was .242 with none on (also, it is .321 with runners on). Averages are usually a bit better with RISP and runners on, but those are huge differentials. The table below shows how the Cards and the league have done in various situations. If you look at the pitching numbers carefully, you can see Cards pitchers are doing a bit better than the league average as well.
To estimate how many wins the "luck" has given the Cards, I used my equation for generating winning pct based on OPS differential.
Pct = 1.21*OPSDIFF + .5
The Cards batters have an OPS of .747 while their pitchers have allowed a .663 OPS. So their differential is .084. That should give them a pct of .602 while in reality it is .644. That gives them an extra 3.08 wins. But they would still have a very good record without the luck.
It is mostly on offense where they are getting their luck. Over the years 2010 - 2012 here is the regression generated team runs per game based on OBP and SLG
R/G = 14.71*OBP + 10.37*SLG - 4.57
The Cards have a 0.337 OBP this year and a 0.410 SLG. The formula predicts they would score 4.64 runs per game while it is actually 5. So that is about .36 runs extra per game, probably due to their great hitting with RISP and runners on. The only team over the years 2010-12 to have a greater positive differential than the Cards this year were the 2010 Rays, who had .45. The next best team this year in all of MLB is the Mets, at .29.
The regression equation for runs allowed is
R/G = 16.95*OBP + 10.67*SLG - 5.41
The Card pitchers have allowed a .302 OBP this year and a .360 SLG. The formula says they should allow 3.55 runs per game while it is actually 3.479, for a difference of 0.071 runs per game.
So combining the .36 runs from batting with the .071 fewer runs allowed, we get .435 total extra runs per game (there is some rounding going on). Over 73 games, that is an extra 31.76 runs. But they are only the 2nd luckiest team so far this year. The table below shows how all the teams have done.