Yes! That's the version I think is best. Also, instead of a random kid asking him it's the bartender that asks him on his way out, which I think makes more sense.

I've heard this joke told a few ways, I think the far superior version is where instead he says "If my horse isn't back by my third drink imma have to do what I did in blah blah blah, and I don't want to do that again"

Makes the punchline hit a bit better.