Not really, especially not if your protagonist goes through a similar set of circumstances. (One of the things Rowling did right) at that point you begin to understand what drives your villain while still seeing what he should have done rather than what he did. yes there may be a little pity, but that overwhelmingly feeling is predominately anger at the villain for choosing an 'Obviously' wrong path.

Rowling's mistake was trying to keep the story 'G' rated, it doesn't work when the hero has to kill the villain in the end, and she apparently missed that memo.