Thanks to another visit to the Wellcome Library I've discovered that fleas do poop. A researcher called Nöller studied dog fleas and commented that "the insect defecated from seven to fifteen times during a feed", "the last material voided being red fluid blood". Nöller also found that human fleas pooped 10 to 20 times in half an hour. Nöller's experimental rig was described as a "circus method of controlling single fleas" and consisted of wrapping the flea with a loop of fine silver wire as shown in the diagrams below.
The text book also covers details of flea mating, experiments in India with regards to rat fleas and disease propagation and a detailed description of the parts of a flea.
Ref: A textbook of Medical Entomology by Walter Scott Patton and Francis William Cragg 1913.