With ours you are allowed to come to more sessions but it's not extra money it's one fee to get in to the club and for the club uniform/patch but it actually gives you a discount on everything else from yearly payments and equipment purchases along with testing fees. So far in my school and those schools nation wide there has not been a student who did not eventually join the black belt club, it's simply logic join and save money lol.
Oh and you really couldn't accelerate how fast you get a belt. You could expand how much you learn but there are months spent training qualifications from belt to belt. It's also a full commitment to getting a black belt and is discouraged if one is not serious. You have to b at least green belt in my school to join.