My cat Snickers (neutered male) had crystals 2 years ago. He nearly died from them due to his age. He was 14 at the time.
He spent one solid week on a catheter; they took the catheter out TWO TIMES while he was in the hospital and he kept blocking up. FINALLY he was flushed and started peeing properly.
He began eating properly within hours of the crystals being flushed and has not blocked up again. And this is in a household of 8 cats, but I watch him like a hawk and am one vigilant mother!
Snickers recovered very well --- given his age. If your cat is young, I think they will have a better recovery. Snicky was put under a total of 3 times in one week and his poor heart barely could handle it. I was SO distraught.
Your kit may have some tenderness down there after passing the crystals. Snickers did, mainly cuz the crystals were so big and the catheter being 'up there' for a week... he kept on licking himself. But he went back to using the box and eating.
Also the diet must change... to the stuff labled for 'urinary tract health' and also "special diet". I didn't buy the expensive stuff the Vet tried to talk me into... thank god too, cuz of the food recall... it woulda been on the list.
I went with Purina.
Good luck, your kit should make it through this just fine and return to normal. If my boy did I should think any kit would. Crystals sometimes return. In Snickers case, they did not.