There's to many variables. The PVA adhesives I use couldn't be used like that because once dried water has no effect, in fact they are washable so a wet print wouldn't adhere. I've never seen PVA adhesives attacked by fungus.
It's more usual to use wall paper paste which is starch based for wet mounting prints, this does need anti-fungants and they are included in all commercial wall paper pastes. The technique you describe would work with starch based adhesives.