I agree with you, ree-Xi, to an extent. But I think it depends on what your definition of "community service" is. I don't do a lot of true community service with the Junior League, but I still consider my work there to be volunteer work. I'm currently serving on a committee that is focused solely on internal operations, but I find the same value in that work as when I've been ladling up food for a meals-on-wheels type of program.
With Gamma Phi, I do a lot of volunteer work, as opposed to purely social. So it is definitely possible, if that is what the alumna member wants to do. For the seven day period of last Monday through tomorrow, I have done or will do the following: attend a chapter meeting and speak to the members, attend alumnae exec meeting and give my officer's report, meet one on one with an advisee to go over an upcoming event, attend a social dinner, pick up a t-shirt I bought to support a chapter's philanthropy, attend an advisory board meeting, and send a bunch of emails to recruit alumnae volunteers for an upcoming chapter event. Admittedly, this is a *much* busier week than normal, because of the time of year and the positions I hold, but it's a good example of what an alumna initiate can do that is volunteer work rather than purely social. Even if it isn't traditional "community service."
OP, I wish you the best of luck!