Yes and no. I agree with @josie that they don’t give as much information as the attention paid to them would suggest and that the tax returns are often discussed at the expense of more important issues. That said, it seems to me that they are relevant for promoting transparency. A politician’s tax returns rarely provide anything even close to a major revelation. Releasing them is standard procedure, after all, and everyone knows it. The monumental hubris of the average politician aside, there is almost always some aide who makes sure during the exploratory phase that any potential campaign will not be sunk by something as basic as tax returns. But this is why refusing to release them or trying to put it off for an abnormally long time is informative in its own way.
Moreover, it makes sense to check whether people promising to manage the nation’s money effectively are capable of doing so in their own lives. These skills do not always overlap; but when candidates spend half their time insisting that their personal character traits are demonstrative of their leadership potential, it’s worth taking the time to see if their character is what they say it is. This connects to what @mazingerz88 said about hypocrisy. There’s nothing so revealing as finding out that a candidate donates money to causes quite the opposite of those he publicly supports. Again, nothing so blatant is likely to happen in the modern political climate—but that’s just one way in which the tax returns act as an early filter on just how many people run in the first place.