Oh, yes indeedy! Clindamycin is the ONLY thing that's ever made my cat quit eating...she had very bad diarrhea and stopped eating entirely (and this cat has NEVER left food in a bowl, ever...she is an iron-gut cat and will eat anything, so when she backed away from her food with her ears pinned back, we had a biiiigggg problem).
It usually resolves as the intestines rebuild their normal chemistry after the antibiotics stop. Plain yogurt or supplemental digestive enzymes can help speed up the process, if your cat will eat them. Sometimes, Flagyl (another antibiotic) can help reduce intestinal inflamation and help get things back to normal (though it is really nasty-tasting and cats don't like it at all). Plain, bland foods (boiled skinless chicken breast, boiled white rice, yogurt, cottage cheese) can help too, by making the digestive process as easy as possible for a few days.
You might want to ring your vet to inform them of the diarrhea; there may be a different antibiotic that could be substituted (especially if this treatment is to be long-term), or they may want to see her for a quick recheck and may be able to help you get her digestive tract back to normal more quickly. I believe in notifying doctors of any medication side effects I encounter (mine or the cat's), just so that everyone's up-to-speed if there are problems later.
But yes, antibiotics can cause diarrhea, and it often resolves after the meds are done, but sometimes the digestive tract needs a little help or a jump-start to get back to normal.