No, the transfer of energy is actually from the conversion of the chemicals from one form to another through the fluid electrolyte between the plates, no reaction can take place in the electrolyte if they're separated. Metal plates allow electrons to flow, they do NOT allow ionic fluids to flow.
Voltaic cells are the magical borderline between electronics and chemistry. Not easy for someone based in electronics to understand, they're very different fields, however they do share some similiarities. Mainly because electrons play a major roll in virtually all chemical reactions.