Upvote:7
Absolutely. In addition to the ship-mill, a watermill mounted on a floating barge that could be maneuvered around just such a channel as you propose unsuitable for a watermill, various types of sluices (including mill race, leet, flume, and penstock) provide means of operating a watermill both away from a waterway's main channel and with a pressure head localized on the mill wheel for greater driving power.
Combined with the steadily greater ability through the Middle ages to gear the workings of a mill, any flow capable of turning the mill wheel could be geared to provide sufficient torque for the work required.