Pay attention never costs you anything; instead, saves you from several problems that can suffer you after you have un-attentively performed any stuff.
Believe me, prior alertness is much better than to solve the troubling situation.
I am thinking that paying attention might have beneficial effects on individual nueron connections in the brain. However not paying attention is also working a part of the brain I would think for imagination. But without focus the mind would constantly wander and you would die from starvation. So not paying attention could conceivably cost you your life.