Lets think about that.

• The rivers flow rate is the product of its cross section times the flow speed.
• The flow rate is also the sum of all the runoff and streams that end in the river above any given point.

So, if what you assume were true, the flow speed would sink. The ingress flow rate would not reduce though, why should it, so the only way to keep the ratio between flow speed and cross section, aka the flow rate constant would be to increase the cross section area. So, the water level would have to rise, no other way to achive that. So the question is: “Will the river in its entire length raise its level when we put these turbines in at any point?” - that would be a great way to get hundres kilometers of deeper shipping lanes for free, but no, of course it won’t.