If it's not a full time thing, I don't see why she couldn't join. I have a friend who makes cakes and cupcakes (mega talented--an artist), but she takes work on a free time/case by case basis and bakes at her home. That may be this poster's biz. Unless she has a shingle on a storefront, she can probably choose when she works. Most sorority girls would LOVE to have a pastry chef among their midst.
In fairness, I've not got gotten a true sense of how much time this takes out of her week.