If you're going for a culture victory, every little bit of culture helps, and choosing to 1) Have no state religion and 2) spread all religions to your three main cities can help add to the culture. So, the missionaries help culture.
Also, the missionaries make it possible to build an extra temple and an extra monastery in the city of your choice, which overall contributes to the possibility of making another cathedral. We're talking a lot of culture, a little happiness, and some science to boot. Very useful in my opinion.