crowded museums in Athens on free-admission days?

My wife and I will be touring Athens in late October and are following Rick Steves' suggested agenda, which involves visiting on day two the Acropolis Museum in the morning and the National Archaeological Museum in the afternoon. By coincidence, this day is October 28, which is a national holiday in Greece, and admission to both of the museums is free. I was pleased at this serendipity, but my wife wondered if we should switch our museum visits to day one because the museums might be extraordinarily crowded, due to the free admission. Does anyone know if museums in Athens are swamped with visitors on free-admission days?