If the top layer of a large river freezes, is the remainder's rate of flow affected?
No, the rate of flow would usually be unaffected. The same volume of water has to get to the sea, so unless the ice was so thick and so well anchored to the riverbank as to exert pressure on the flow of water beneath, which is very unlikely, the rate of flow would remain the same. If, in the unlikely event that the ice exerted pressure on the water, the rate of flow would speed up. 

It's the same when you pinch the end of a garden hose. The same volume of water has to get through a narrower opening, so the jet becomes smaller but faster and more powerful because it is under pressure. For your purposes a faster flow would help your turbines to do their job but as I say, icing conditions are rarely such that ice would exert pressure on the flow. The friction between the current and the relatively thin coating of ice which usually occurs would not be enough to have any noticeable effect on the rate of flow.