I cannot definitively say yay or nay about them but based upon my experience in raising 25-30 baby, orphaned Muscovy ducks, I would say they do,
When they were little, they would wander around picking mosquitoes off the under side of leaves...they would jump up to grab spiders from the underside of a cap block on a knee wall...any sow bug climbing the wall was a sure goner. One of them - Bo - could spot a moth miller from 20' away.
They had a large mortar tub filled with water for bathing. The ground under it was always damp from their splashing and when I would dump it to fill with clean water, there were always worms...the ducks would come running.
When they were at our pond, they spent much time rooting around the shoreline grabbing invertebrates/larvae including small crawdads. One of our cats sneaked out onetime and I was trying to entice him back in by tossing him canned tuna. He never got any, the ducks ate it.
That doesn't mean they didn't eat plants, they grazed on grass like a herd of goats. Loved lettuce. Peas and corn too, especially corn.
All the above applies to Peking ducks too, had one of those for a while after an alligator or snapping turtle had taken off one lof her legs.