Answer
No.
Work Step by Step
An ordinary fan does not cool the air in the room; In fact, the motor gives off heat which raises the air temperature slightly in the entire room.
However, the fan helps your sweat evaporate by circulating air. It is the higher-energy water molecules that leave first, lowering the average temperature of the liquid that is left behind. This cools you off, though overall, the system of you + room gets warmer.
Furthermore, as the fan moves hot, humid air away from you and lets cooler, drier air move in, this also assists in evaporation.