I have researched drowning fleas. There is a lot of good data at Can dish soap really be used to kill ticks and fleas? the summary there suggests if you wash fleas away in the yard, your pet well get them back tomorrow. But if you wash them down the drain they are gone forever.
There are multiple online reports of "drowning fleas" and killing them with soapy water. After looking for the science there does not seem to be much support for these fatal claims. There is little doubt that giving your pet a soapy bath in the tub will help remove the fleas, they may even appear dead. But in all likelihood these fleas are just waiting to dry out and be revived, hopefully in the city sewer. If you bath your pet in the yard, and than let the dry pet in the yard again the next day the clean pet and clean revived fleas will likely reunite. Soapy water is more likely to facilitate removal of the comatose flea from the pet and carry it down the drain. So it is reasonable to have noticeable decrease in the flea population after a bath. But excessive bathing has it's own risks and given the life cycle of a flea soapy baths alone are unlikely to be a final solution.
I believe some insects, like spiders if flushed or washed down the drain will often climb back up into the home.
Does the same hold true for fleas? Does flushed = "Gone" or "On a short trip, be right back"?