The short answer to that question is, yes. Here’s why:
Many people think that covered litter boxes will reduce the smell. It may reduce it for the human but it increases the smell for the cat. If the box is too stinky, a cat (who is a very clean animal) will find an airy corner or fluffy pillow to do their business.
I have a proven way to reduce the smell. Clean it daily or twice daily. You could also put a small open container of baking soda near the litter box (you can also sprinkle it directly into the litter) to absorb some smell. You can’t expect it to smell like a bed of roses if you only change it every few days. I clean the litter boxes twice a day. It takes about 20 minutes total and it definitely reduces odors.
Another reason why covered litter boxes can cause aversion is because they are usually too small. A cat should be able to turn around and have enough room to dig. You want them to dig because then they will cover up the source of the smell. If it is too small, they will do their business and just jump out leaving it uncovered.
An automated litter box sounds like a good idea but it’s not. What if it starts when the cat is still in it? Consider that to be the last time your cat uses that box. Cats are very sensitive about litter box issues and they certainly don’t want to be surprised when they are doing their business. Another thing about automated boxes…you don’t see how much or how little they are urinating or defecating. Too much urine could be a sign of diabetes, too little, could be a potentially life threatening urinary tract infection. It’s a little gross but it’s true that you can tell a lot about the health of your pet by looking at what comes out. If you have a machine clean it for you, you could be missing signs of poor health that are in the beginning stages.
My advice? Get a storage container, not a litter box. Give them a lot of room to move around. This will also be more forgiving if you forget to clean it once in awhile. Fill the box with at least an inch of litter or as much as three inches. If you are worried about them getting litter everywhere, get a storage container with high sides, take the lid off and cut a large hole in the end or on both ends. Cats want to know they can “make an escape” if they need to. If you have a multi-cat household, two holes may be a good thing. If a cat is blocking one of the exits, they have the other exit or they can just jump out of the top (although they could tip it over).
Also, try to avoid scented litter. Cats can smell much better than us. You want them to be comfortable in their litter box, not trying to get out as soon as possible because the “gardenia” scent is so overwhelming.
So, get a bigger box than you have now, with no cover, unscented litter and clean it at least once daily. With that combo, you should have a odor less house and one happy cat!