No, fireplaces cannot earn the ENERGY STAR label.
Wood stoves also cannot earn the ENERGY STAR label.
Biomass stoves may be eligible for a tax credit. Biomass stoves burn biomass fuel to heat a home or heat water. Biomass fuel includes agricultural crops and trees, wood and wood waste and residues (including wood pellets), plants (including acquating plants), grasses, residues, and fibers.