The fan won't make it any cooler than the air around it.
If the air movement caused by the fan were to be actively evaporating any dew condensed on the sensor then that would make the sensor read lower than the surrounding air, potentially by quite a noticeable amount. This would obviously only be a transient effect, ie until any residual dew had evaporated, but it would potentially be real for as long as the dew lasted.
But as I alluded to above there are several second order effects to consider in FARS vs passive. It does also make a difference where in the world you're located. In Northern Europe (lower max solar irradiance, usually more breezy conditions, daylight hours often too short in winter to recharge solar power adequately), I'm not sure that the cons don't outweigh the pros for a FARS, or at least for the 24 hour FARS - the DFARS is more debatable perhaps. But if you're in eg the Southern US then the issues might well weigh differently and very possibly in favour of the FARS.