I have a .4 acre shallow old pond that is nearly covered with American Lotus and I know there is some coontail also. Would draining the pond help in any way to kill off these plants? Would having it dry over the winter kill them in and of itself?

I doubt it. If the pond bottom stays moist, even a little bit, enough of the plants will survive to repopulate the pond once it fills up again.

I wonder if Grass Carp would help to eat your plants?

That is a solid no by killing it with one winter of dry bottom. Tubers can handle frozen ground here. You also likely have a seed bank even if you kept pond dry a couple of years.

Heavy grass carp pressure next spring as new shoot come up may get you in desired direction. Stocking young carp will not get it, they need to be 5 lbs or better.

You might get control by keeping hogs confined on it.

You could get rid of it completely by draining and dozing out the sludge, plus a few inches underneath, but only if you are in good clay, so as not to cause a leak.