I just don't think the physics pan out here. First off, the amount of air needed to get a fan spinning will sap the energy from the lungs pulling in air and instead direct it to trying to move a stationary fan. Secondly, having a pop can making the air pathway larger decreases pressure or power of the suction due to increased volume. So say your baseline with a regular atomizer (whichever one it is) is benched to be 100%. Even if the fan were to help somehow, you've lost more than 50% of suction/vacuum (pulling power from your lungs) by the enlarged soda can id. Playing devil's advocate and saying for purposes of the argument the fan helped at all.. and provided 50% assistance. Look where you're at, back to the same 100% starting point.
It will make the process more complicated with no benefit. If the goal is to make inhaling easier, the atomizer needs to change. Larger air inlets, larger chimney, larger drip tip. But since the capacity of the lungs is fixed and finite, this just means more volume moving in a shorter amount of time. Ie, a 5 sec puff reduced to a 1 sec puff, inhaling the same amount of air. And if the coil diameter/surface area and power don't change, all you're doing is adding more air to a given amount of heat, reducing vapor density. A big lungful of wisp instead of vapor.
Chances of the lungs inhale vacuum created being strong enough to spin a larger fan (the size of a pop can) is about nil. Air follows the path of least resistance and would simply float around the fins of the fan without even nudging it. That's why when it comes to things like pc fans (disregarding the fact they're powered), the smaller fans at higher speeds produce more pressure with more sweep to the fins providing higher static pressure. Consider trying to vape a column of vapor produced by a small table 'turbo fan' vs getting a column of vapor from a lazy big ass ceiling fan. A powered fan would provide assistance, an inert powerless fan just becomes an air obstruction.
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