No. The cars would be doing a little extra work. Imagine if you did it with half-filled hoses of water going in a loop. The car tires would be pushing the water through the hose, adding drag. The energy cost would come from the gas or electricity of the car.

It's like the usual analogy I used to use for content mills or adtech: it's like setting up wind farms along the interstates. The wind from the trucks creates free energy! Awesome, right? Except that those trucks are no longer drafting off each other quite as much...

(And I say "used to use" because it used to be a small tax, a bit of an extra nuisance here and there, and people largely felt like it didn't really cost anyone anything. Now it's more obviously expensive, like making the entire roadbed out of little rolling wheels that charge generators, so you have to "drive" 80mph in order to progress at 50mph...)

It takes more energy to drive a car through mud than on pavement. The same principle would apply here.