The fan will definitely spread mold spores but the mold is there because of stagnant moist air. The only way to make the area inhospitable to mold is to provide - good air circulation, low humidity, fresh air exchange.

It won't matter where the spores land because the air flow created by the fan would will prevent the spores from taking up residence and reproducing. Mold is always there, just waiting for the right conditions.

What are you going to spray with?