Yes, it does. Any extra-curricular activity shows that you are actively engaged and can take the initiative to do something outside of school. Of course, the most valuable extra-curricular is sports, but that's not the topic here. Depending on how many other things you do, it'd be a good idea to follow up on the offer, but only if you don't have to rearrange every detail to go with it.

Benefits would vary with the situation and the purpose of the club. I can imagine free food at least once. You'll have to ask.