The wiki states that the lucky foot raises luck. Unfortunately, it fails to state just what that means. So, what does raising my luck do?
The Binding of Isaac – What Does the Lucky Foot Do
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According to the wiki, the only item that seems to be able to raise your stats above the maximum is The Sad Onion, which doubles the firing rate no matter its current value. I have very little personal experience with that item, so I can't confirm or deny this.
The stat that I find easiest to max out is damage, as I've often managed to get quite a few damage enhancing items in a single run (which would have put me over the maximum looking at the bars in the pause screen). I always seemed to hit the same cap, no matter how many damage enhancers I picked up.
In light of the above, my previous version of this answer indeed states that the item is useless once damage has been maxed. Further research, however, proves that I was mistaken. To test this, I played with Judas, picking up both The Pact and Pentagram, which maxed out my damage. I then engaged the boss Gish. Here is Gish's health-bar before I started measuring damage:
I then shot Gish three times, bringing him down to this:
The difference was 11 pixels. Then, I used the Book of Beliel and shot him three more times:
This time, the difference was 15 pixels.
So as a matter of fact, the Book of Beliel can and will take you above max damage.
Sadly, this experiment doesn't give a single conclusion about the multitude of other ways that one may try to raise his stats past the maximum, but strictly speaking, the answer to your question is yes.
It's actually in the wiki:
??? | Character | Defeat the boss in The Womb 2 for the tenth time.
Best Answer
In addition to the other answer, I have experimentally found that the lucky foot increases the chances of winning at the shell game in the arcade. The wiki says that the probability of winning on any single run is 33%, but when playing as Cain I have recorded a greater than 50% win rate (so far it seems to be 66%).
Edit: according to discussion on the item page on the wiki, the foot also makes you only get good pills. The comment said that collecting it turned a bad pill into a good pill like the PhD item.
Edit 2: it appears that the Womb levels decrease or nullify the effect of the Lucky Foot. I went to an arcade on The Womb 2 and found that my win rate was below 50%.
I tested with 140 consecutive runs of the shell game in The Womb 2 and I won 77 times, so it looks like the win chance is a bit over 50%, but definitely not 66%.
In addition, the lucky foot increases the chance of getting an item from the beggar. Without the lucky foot, it often takes 4 or 5 coins before the beggar will drop a single item. With the lucky foot, however, I have never seen it take more than 3 coins for him to drop something.