I think that is a correct assumption.
Case in point.
Clients pond up here. Floating mats of FA, Sago Pondweed and Curly Leaf Pondweed growing to the surface. FA growing on the plants too. Water clarity 30+ inches, and weeds are growing up from the bottom of the pond in 4 1/2' of water. Eutrophic pond, LOTS of nutrients in it. Clear water is causing a lot of problems plant wise, and 1/2 of the pond is unfishable.
Used a liquid herbacide to kill the plants, and Cutrine Plus (both liquid and granular) to kill the FA. Stocked Tilapia at the rate of 40# per surface acre. Blues for a couple of years, then Hybrid Mozzies after that. If the water temps were right to get the Tilapia in early, I didn't have to kill the FA or plants first. If the plants and FA got a good head start, then I had to kill 'em.
The water clarity dropped to 12"-18" due to a planktonic algae bloom. FA only grew in water that was too shallow for the Tilapia to swim (VERY little of that) and no vascular plants grew from the pond bottom due to the reduced sunlight penetration in the water column.
The amount of Tilapia to stock all depends on how much FA you have. Only a few years of experience will tell you how many depending on the amount of FA and the amount of nutrients in the pond. I tested different stocking rates, and found that killing the FA, then stocking 40#/surface acre works up here.
