The scoop really doesn't create much additional pressure to the tubes and the main function of the scoop shape is for creating a stratified flow to the upper deck. A small amount of additional pressure is created from the scoop depending on water speed and is called stagnation pressure. A simple test of this is to take a funnel with a short hose attached and put it into a stream at different flow speed locations and raise the hose above the waterline and see what additional pressure is created causing lift (not much). The main pressure to provide flow in the tubes is from the head pressure difference in height between the scoop inlet and the tube outlets. So lets say if you only need 4 inches of head pressure to run the sluice well, you could locate the sluice in a spot that gives you 3 inches of head drop and 1 inch of stream stagnation pressure for a total of 4 inches of pressure. The speed of flow required to create 4 inches of stagnation pressure would be very fast and isn't realistic for a stream (and your sluice would go bye-bye). A 1" increase in pressure is around 3ft per second and is possible. So finding a spot with a couple inches of drop is important part to gain the majority of the total pressure needed.
I do want to thank you for defining stagnation pressure. That exactly defines what's going on in the scoop. That'd be the kinetic energy stored by moving mass, and when the mass is stopped, the energy is converted to pressure. True?
Are you saying that the difference in water pressure from a couple of inches of drop accounts for the main pressure applied at the tubes? That'd be the same as a two inch water column, wouldn't it?
At any rate, if you were to remove the funnel from your hose, the stagnation pressure would not be practically nothing. It'd be comparable to putting a finger into a running stream to stop the flow, and putting the palm of your hand in the stream to stop the flow. You'd certainly notice the difference in pressure. Would you agree that the difference in pressure between the water in the tube, and the water in the trap is what makes it all work? If so, then it'd seem that the BGT should work the same whether it were submerged, or not. Wouldn't you agree?