Apparently so. I "shot" a doe, mid-body and behind the shoulders, with a 270 rifle, 150 grain Nosler Partition, within 30 yards, off of a steady rest. She kicked and took off like a scalded dog. I followed her until she disappeared into the trees and moguls of ravines. I went to the spot where she stood and found nothing. No hair, no blood, no meat, no bone. I searched for three (3) hours until after DARK and found NOTHING. Days later I went back expecting to find a carcass. Instead I found NOTHING once again.
So, from a statistically insignificant population of one, and yours makes two, I would say YES, they kick even when NOT SHOT.