— Well... If the kids want to organize such a club, why not? After all, "the kids can do all this anyway" applies to clubs in general. The only small problem I see is with the name. Perhaps if it's changed to something else, all the other questions will resolve themselves. For example, I don't even know... Some kind of "exam preparation" club, or "improving academic performance" club, or "extracurricular activities" club, or "additional learning" club - although the last one doesn't sound very good, but whatever. In general, let them choose one of these options and it will be fine. Again, maybe someone would want to join it for their own benefit, but they might be embarrassed by the word "underachievers." But that won't be a problem this way.
only based on passing the exam with a satisfactory grade or higher, and thus, in the absence of additional classes, or for those who are not initially unintelligent, if they join, the OS (presumably referring to a game mechanic) can be replaced with a bonus to intelligence. I think it would be role-playing appropriate, balanced, and not exploitable