I can see a way to "cheat" on this if the fan unit has to stay attached to the electric motor

The fan would have very low thrust so any vehicle would need to be as light as possible to get much acceleration and the fan itself won't be very efficient anyway. Using the fan to drive a turbine (presumably connected to the wheels?) would be even less efficient.

What you'd want to do is make the most of whatever power the motor can produce. First off, no matter how you do it, the vehicle has to be as light as possible so use balsa anywhere you can. Aerodynamics won't have any affect at the speeds it won't be capable of . Then I'd blank off the front, back and ends of the fan with light cardboard or whatever so the fan is totally enclosed and not have any air drag. Attach a small pulley to the fan shaft and another pulley on one of the wheel axles and use a rubber band to drive it. Play with pulley sizes until you get the best performance (the rubber band will allow for any differences in sizes).