Usually, but not universally. Some high drag, low performance aircraft when at MAUW move so far along the basic polar curve that the ideal L/D can occur at above Vne. However for 99% of aircraft there will be a speed that will that will be best L/D at a higher all up weight that will match the line for best L/D at a lower weight.
Some modern high performance gliders actually achieve a better L/D with full ballast than at a lighter weight.