Yes and no.
My thought experiment posits a motor directly connected to the wheel, via gears if you like, but in a completely linear fashion where the wind can cause an un-powered motor to rotate in either direction.
But even with your one-way gearing, you will need more than "any tiny bit of power" to get the motor to turn. The motor needs to generate sufficient torque to overcome the (head wind) wind-force. Whatever your gear-ratio, there will be some minimum amount of power needed to make the motor spin. Otherwise the motor is stalled and power turns into heat.
The distinction between torque (rotation force) and power is where this thread was coming unstuck before.
Suppose, for a moment, that we have ideal, frictionless gears. It's not going to happen in the real world, but suppose we have Teflon gears and roller bearings and whatever.
Now, suppose we wish to move our vehicle forward at 0.1 m/s against a 100 N force of headwind. We can calculate the required power as 0.1 x 100 = 10 W. So, if there are no losses in our ideal gear train, then the motor needs to output 10 W to achieve this rate of forward progress.
If, maybe, we only have a 1 W motor, then we cannot go this fast. However, we could go at 0.01 m/s, since 0.01 x 100 = 1 W.
How big the motor is determines how fast we can go, but if we just want to go at any speed at all, then we can introduce ludicrous gear ratios and make the motor as tiny as we like.
This is why I say "any tiny bit of power". In the real world, of course, some power is required to overcome the friction in the gears, and more gears will have more friction, so there is a law of diminishing returns. However, in principle, a wind up clock mechanism could make a vehicle move against a gale force headwind, albeit at a glacial pace.