Yes, although your question doesn't state whether the magnets have to be in the vehicle itself or not.
1) Magnets are in the car. In this case, it would be much more efficient to use a well-designed flywheel, rather than taking the spinning magnets' energy, converting it into electricity via a dynamo, then converting it back into mechanical energy via a motor. Flywheels have to be specially designed to not explode when they're spun fast enough to power a vehicle for any length of time, and it would be much harder with magnets.
2) Magnets elsewhere. After all, much of the electricity produced in the world is via steam or hydroelectric power. Both of these spin magnets in coils (or, more likely, coils around magnets) and the resulting electricity gets shuttled to your house via electrical lines. There is CERTAINLY enough power there to run a car.
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Ah. The rotating magnets would add a LITTLE energy to the situation, but very, very little. Certainly not enough to drive the car one mile on very level pavement. So there's little advantage (and lots of disadvantage, like moving parts to break) to having more things rotating.