Not strictly necessary, but nice to have once they're eating solids. My 11-month-old's poops are sometimes solid enough to just shake off into the toilet, but not always, and swirling is gross. Water drips on the floor, and it's hard to get it all off no matter what you do. I don't actually have a sprayer, but I did start using flushable diaper liners, and they make a huge difference. You're probably going to want something once they get past the runny poop stage.
happy, you don't need a catheter and bedpan if you have a diaper, silly! Srsly, though, there are sprayers attached to the toilets at the hospital where I work, and we use them to rinse out bedpans, as well as the jugs used to empty catheters. So I guess my answer is yes!