Putnams Airspeed Aircraft since 1931 by HA Taylor mentions this particular aircraft, the only AS5C. Delivered in 1934 it was used for test and demonstrations with the 16 cylinder Rapier 4 of 350 hp.
It was re-engined with a Lynx IVC and operated by Portsmouth, Southsea and Isle of Wight aviation as a AS5A before being impressed as X9346 on 18th March 1940 and used by the ATA at White Waltham and Hawarden until being sent for communication duties at Airspeed 13th March 1941. It was sent to 5 MU on the 18th January 1944 but was struck off charge on the 12th April of that year. Unfortunately there is nothing about a contra-rotating propeller. For what it's worth, I have never heard of such a mod - but absolutely anything is possible in the wonderful world of aviation!