Sorry but no
This would devaluate the value of the medal.
This is the civilian equivelant of the V.C. and the V.C. is not given to everyone.
The NHS staff are working in very difficult and at times dangerous situations but are certainly not worthy of being awarded the G.C.
Those NHS members who have died in the cause of fighting and saving lives perhaps should be given some award but even then not a G.C.