Welcome to Paddleducks Andy,
The feathering mechanism on a paddlewheel in simple terms keeps the paddle blades vertical as the wheel turns and they move through the water, so giving more thrust. In model sizes I don't feel it has any great effect on performance (others may disagree?), it just looks "right".
Having said that it looks "right", bear in mind that the top half of the wheel is covered by the paddlebox, and most of the lower part of the wheel is in the water, so any feathering mechanism cannot really be seen!
I've built models with feathering mechanism, and none feathering wheels, and both perform equally...
Hope that helps?
Regards
Eddy