As Brad said, a club is a great way to meet new buddies, and get more diving done. But running one does take a lot of support and commitment. I've been a committee member on a number of non-profit clubs, and by and large the attitude from members is "you're the committee - you make this club fun!". But as long as the members want to be part of it from the start, that shouldn't be a hassle.
Now, speaking from experience from the dive club at my high school (many, many moons ago!).. One of the phys-ed teachers was a keen diver, so he was running the club mainly for freediving and spearfishing, but seniors could go out on scuba. Through much fighyting over the years with the Powers That Be at the school, the club was eventually disbanded due to high risk (or more so, fear of the unkown sport by the principal - never saw someone rushed to hospital after receiving a shot-put in the back of the neck while scuba diving!), or more so liability insurance.
So if you want to start a dive club at school, you should certainly do your homework before presenting the idea to whoever needs to approve the club.