Dynamic range in the energy meter specification means current dynamic. Voltage will be nominal mains voltage plus/minus expectable variations. As a result, all current spectral components except a small band around the fundamental will be filtered out when multiplying current and voltage and integrating over full 50/60 Hz periods. Low-pass filtering will further reduce the effective noise bandwidth of instantaneous power measurement to a few Hz. In the energy integral, you finally have mHz noise bandwidth.