Only in manga you will not get reported and publicly shamed if you try to approach a woman in gym 😄
I'm kidding of course. If a woman is attracted to you she will forgive you anything.
There is no reason not to.
He is doing it out of respect and to learn things he can not on his own.
Even if the things are not super useful for him, he can teach it to his Bride Army, WHICH HE ACTUALLY SAID.