Well, that's a tricky question. It depends on the cat, how bad it was etc. But, even after the UTI has cleared up (I would guess average time is a week or two) they may still have litter box issues for awhile. A) they are still sore B) they associate the litter box with pain and C) they smell urine in other places and think it's okay to go there. Therefore, it's extremely important to make sure you thoroughly clean all the areas she's peed on with a good enzymatic cleanser like Nature's Miracle. Check out the sticky at the top of Behavior "Things that Saved My House..." It'll give you a great stop by step of how to eliminate urine. You can also try Cat Attract litter and most importantly, give it time. Once she's truly feeling better, if she always used it before, she should go back to her box.
One of the very best things you can do for her right now is to make sure she gets LOTS of moisture in her diet. I would make sure she is on an all wet, high protein diet (at least for awhile) and even add some spring water to her food. It is THE most important factor in avoiding and treating UTI's.