A few operators seem to be using them;
Air Ambulance Worldwide - Air Ambulance Aircraft
although I'm not sure they are for the same type of operations as the RFDS, and the Italians
GDF: Piaggio Aero Industries has delivered two P.180 Avanti II aircraft to the “Guardia di Finanza, Italy’s Border Patrol agency... .... In order to meet customer requirements, the P.180 Avanti II is equipped with an Ambulance Kit, which, through a quick reconfiguration, allows the aircraft to become an efficient air ambulance unit.
just
possibly influenced by the fact it's a domestic product, as the article goes on to say,
The deliveries are in the wake of all the other Italian State Air Services, the Carabinieri, Vigili del Fuoco, Army, Navy, Air Force, Civil Protection and Corpo Forestale all having taken delivery of Avanti’s.