I gotta disagree with you there JR. Unless the media was already at its maximum capacity for handling flow, the extra velocity probably wouldn't cause any visible congestion. There is a CHANCE there could be some acceleration happening there... but as my calculations already showed, even under "ideal" circumstances it's very little. Definitely too little to see the difference with the naked eye. I would think the most likely visual cue of a change in velocity would be the amount of splashing. If the water is falling faster, it should splash more and higher in the lowest tray compared to the second from the top (not the top, so we're still comparing the same distribution of water). However, whether this is a large enough effect to be noticable is questionable.
I have my doubts as to whether there's any actual velocity difference or not. It all depends on the dwell time of the water within the individual shower sections, which I guess you could get some handle on by turning the shower off and seeing how long it takes to stop flowing.
As a physics guy, I love this discussion because it's getting people thinking critically about what's really happening to the flow here. I propose a little thought experiment just to get our noodles cranking. Imagine water flowing in a thin sheet down a flight of stairs. When water falls from one stair to another, it splashes and changes direction. In the middle of the stair, all of the energy obtained from that fall is now pushing the water horizontally. When the water goes over the edge to the next stair, there's no reason for that horizontal motion to change direction, so the energy of the fall to the next stair comes only from the current height, and not the previous height of the staircase. Therefore, the speed when it hits the bottom of the next stair is THE SAME as what happened on the previous stair. No matter how many stairs you stack up, the velocity at the bottom of a given stair will be the same.
The question then becomes, does the BHM act like the set of stairs, or do the curved surfaces allow the water to always maintain a bit of its vertical velocity and hence increase due to acceleration? Unfortunately, this is an incredibly complex question and answering it would probably be a calculation worthy of publication

It IS fun to speculate, though.