I don't see the cart moving in the wind, until it's pushed. The man-carrying jobber-does, that is.
The push begins to turn the prop, otherwise there isn't enough surface area on the propellor to act like a sail.
The models are much lighter, and easier to move in a wind. Much less mass per propellor area.
I think the cart will accelerate to the speed where the wind coming into the prop begins to cut the thrust, as it would on a windmilling prop on a plane, which can be severe enough to cause problems with forward flight.
On my electric r/c planes, a windmilling prop is turning the motor due to the incoming airflow, with a direct drive. That produces sufficient drag on the plane to alter it's flyability.
If the motor isn't braked electrically to a halt, where the prop provides a minimum amount of drag, the plane will descend faster with the windmilling prop.
A free-wheel device which separates the prop from the motor is a better choice.
The prop still windmills, but it's at a zero-slip, zero thrust and low drag condition, relative to having the coupling to the motor.
The best choice is a folding prop, and even these may not fold if the speed can't be reduced to where the wind forces the prop to fold, instead of windmill.
On the internal combustion motored models, a windmilling prop with the motor off is rare, due to the inability of the incoming airflow to move the prop against the motor compression, although I have one clapped-out 2-stroke that will windmill power off, in a dive.
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I'd love to see a chute powered cart.