depending where you live of course, but leather will dry from water quite fast when worn, water actually pooling down toward the hem and cuff pretty fast, faster than jeans.
upper part of the jacket will dry very fast, so if you wear it unzipped, and just walk or ride with the hem of your jacket blown by the wind, it will dry very fast, unless your liner is quilted and soaked... then it will take eternity probably.
This!
I hate carrying an umbrella, and I don´t mind walking in the rain (not that I am after it, but the occational shower while running errands is a non-issue for me), so leather is much more suitable than cotton or wool which soaks up the water and stays wet for ages.