I like your logic
That paddle wheel is in continuous operation. Lets just say it reduces speed by 1/100 of a mile per hour. 1/100th of a mile is 53 ft. For a typical 5 mile race that is 265 ft. - AND you can have that 265 ft with no investment or applying any skill! I have been in a lot of races that were decided by less than 265 ft. Now, I do not know if the 1/100 of a mile per hour is at all accurate, but any speed increase adds up over time.
But the math is wrong
Let me put this even more in perspective.
(I used to service instruments so I know this real well)
If you take a raymarine paddle wheel and blow on it, it will read between 6-12 knots, depending how hard you blow.
So, put your hand in front of your mouth.
Blow real hard. That's the drag at 12 knots.
The water resistance is so small, it's immeasurable.
So, while I appreciate that you don't throw out any racing advantage, the paddle wheel won't do anything.
In comparison, the effects of a prop are huge. If you don't have a feathering prop, it's like towing a bucket behind your boat.
Not to mention marine growth.
Btw, just to put some numbers on things, the older knotmeters used analog dials. The full scale reading was typically 12 knots.
On the simple units (signet, etc.) the paddle wheel directly powered the needle through a diode & capacitor to take out surges.
The meter was full scale 100 micro amps.
(Micro Amps are a millionth of an amp)
The smallest red led needs 10 milliamperes just to get visible light.
A milliampere is a thousandth of an Amp.
An incadescent tiny flashlight bulb takes about 1/10 th of an amp, and it barely gets warm.
If you're a Newton fan, the old ruie is energy can't be created or destryed; just transferred.
So, now think about how much energy 100 millionths of an amp really takes out of a multi- ton yacht going at 5 knots.
Not much.
Ok,,, I'm done.