I wonder how fast a cat would disappear when he responded and seen a dog setting there.

I would think "in a blink of the eye"! I do know this, if a bobcat is coming in on a set and then a coyote shows up, the cat retreats in a hurry! Had that happen once while calling in the N.E. corner of KS. a few years ago. Bobcat was coming in slowly, then along comes a pair of coyotes! It was wierd how it happened, but the coyotes actually saw the bobcat and actually went after it. We wondered later if the coyotes actually thought that the bobcat maybe had the rabbit that they had heard! We never even got a shot fired at any of them[:@]

I suggest not bringing your dog on a cat hunt.