I see no real problem with that. Things to think about:
The post will probably last longer.
Make sure the post is completely dry before painting. when I was a kid, that's what my dad made me do because otherwise fungi would grow under the paint.
Pick your paint carefully to make sure you aren't poisoning the soil/your plants.
If the plan is to have the hops climb up the poles, make sure its not creating a slippery surface the bines can't grab.