Any process that activates or increases the rate or extent of hemocyte proliferation. Hemocytes are blood cells associated with a hemocoel (the cavity containing most of the major organs of the arthropod body) that are involved in defense and clotting of hemolymph, but not involved in transport of oxygen. An example of this process is found in Drosophila melanogaster. [ GOC:mtg_sensu GOC:bf ]