Yes. The longer poles drag the field's return path down. It changes the shape of the field up top, at the string because of it. But also changes the stray flux that puts information in and around the underside of the coil too. You can cut the screw poles shorter if you like, but you might like them long.
The shape of the pole, slot head vs. hex head has a smaller impact on the sound, not enough to be concerned with in my opinion. The length trumps the head shape. But if you trimmed them flush, and it still sounded different, that's why.