This answer is a work in progress, quality science on the subject is proving difficult to find.
First part of the answer - Yes fleas (Siphonaptera) can be drowned. But not as easily as the internet would lead you to believe.
There are many claims on the internet (and printed works) expounding on how simple it is to drown fleas. The best science I found so far on the topic is in Forensic Entomology: An Introduction By Dorothy Gennard; John Wiley & Sons, Apr 30, 2013; section 4.3 which reflects a 1985 work by Simpson K. (Journal of the New York Entomological Society 76: 253-265, not finding this online). Gennard is using the fleas present on a human body at death to determine how long the body had been submerged. Findings -
- A flea submerged for up to 12 hours will appear to dead, but can revive in about 60 minutes after being removed from the water
- A flea submerged for 18 - 20 hours will appear to dead, but can revive in 4- 5 hours after being removed from the water
- It takes 24 hours of full submersion to fatally drown a flea
- Side note; lice (Phthiraptera) can be fatally drowned in about 12 hours.
Second part of the answer - Yes soap can facilitate the death of fleas in bathing
So far the best I have is Medical and Veterinary Entomology by Gary R. Mullen, Lance A. Durden Academic Press, Apr 22, 2009
- This work suggests the process of washing the flea (and the pet) removes integumental waxes on the fleas body and they die from desiccation (dehydration).
Again this answer is a work in progress, while it provides valid challenges to some "internet knowledge" it is far from a complete answer to the question.