I've lived with people who did that. You put a used diaper in the toilet, and do a couple stir and flush cycles. Then you put them in a bucket with detergent. Once a day, you hand wash those, and hang to dry. With about 20-30 diapers total, you can manage.

But damn, finding used diapers in the toilet is annoying. Plus wet diapers hanging all over to dry. If it's your kid, though, it's not a big deal.