Does the martial arts teach us self-discipline?

In a word, no. Often promotions use "learn self-discipline" as a part of the sales pitch but no one can teach another person self-discipline. It is something that you develop within your self. I can't give it to you and none of the Sensei can give it to you. We can demonstrate it, we can explain what it is and we can provide a person examples that would teach them the concept but true self-discipline cannot be taught.

The systems we practice take a bit of self-discipline to master and the practice of a martial system is one way to teach yourself the self-discipline necessary to master it on a personal level. Self-discipline is how you control yourself, the willpower you display in doing things. It is a matter of making yourself do things when you should, even when everything screams in your mind to skip it this week. Self-discipline means self-control. It is doing what you don't want to do when your mind  and feelings are telling you to do something else.

It is developing a trait that says, "I will restrain my behavior or emotions (self-control), activate myself (self-motivation) and direct my personal path, way or road through life (self-determination).

I explained it somewhat here. Now ask yourself, do I have greater self-discipline? Likely, not, but you did show some discipline in reading the entire post when the monkey brain was screaming in your ear, forget this crap ;-)

Self-discipline = self-control + self-motivation + self-determination