It's difficult for me to give crit on t-shirt design (so many factors to consider!) so hope you don't mind me giving my say anyway.
(The following may lean towards more opinion-y than crit-y, but hopefully it gives one opinion towards your question, and that others will jump in as well with theirs so you get a better idea!)
I think it's wearable! Since it's just initials it doesn't scream out club - there are a lots of shirts like that with not particular meaningful writing but just looks cool (o.O I have a zip-up that says thunder bird varsity or something like that?? lol!) so I think it works outside of the club! My stance is "it's 100% okay for OSL member to wear it outside of OSL but not sure if it works as a stand alone design like for selling to general public (though my t-shirt taste probably not representative of the general public so take that with a lotta salt haha) but that's most likely because it is aimed first at club." I think the major thing that gives the club-feel for me is the very distinct colors that work great for that kind of thing but not sure elsewhere.
Some random things that may or may not help:
-I think the sun-glare over the text maybe should be removed as it hurts readability and I'm not sure if that kind of effect print well.
-Not sure if this would make a big difference but, I like the asymmetry effect created by the higher blue oval and I think it might be better for the text to be central on the lower blue circle since it's off center by a small amount and then the asymmetry will be more defined and the oval circumference won't be so close to the 8's outline.
This sounds really cool! Have you done other t-shirts?