If i remember correctly from the game! [It has been a while since i played it] Cait Sith was a electronic type animal, some one from Shinra(i think, i can't remember his name, was it Rude? Correct me if i am wrong)! So Rude, or whoever, was controlling Cait Sith! So unless Rude, or whoever, starts to control Cait Sith again, then you will see him/her! But if he doesn't, then no, you won't see Cait Sith!

P.S. If this is all wrong, please correct me! If it is just the name wrong, still please correct me! I can't remeber that well because i finished the game a long time ago!