As a guy who hangs out with people who regularly (not often, but regularly) wear plate mail, I find this unlikely. Most of them, if the armor is properly fitted, could likely swim in the stuff. It wouldn't be pretty, but they could do it. Someone who was clumsy enough that they couldn't stand up in the stuff would be dead meat on a battlefield.
Alternately, in the military I had to swim 50 meters with 30 kilos of gear (more than the listed weight of plate armor in the phb) before they let me out of training. I'd imagine a knight would have an easier time of it, as their armor was more evenly distributed than my kit.