"Yes and no, I suppose. It's nothing you'd usually feel or notice. But there are legends of people getting powerful enough that they can feel individual living things, from miles and miles away, if they concentrate. That would take a ton of control and raw power, though, both." Which means most people, by the time they got to that point, would be pretty scary, regardless of intentions.

From what Buffy's hinted, Willow might get there one day.