A little. The fan runs around the clock on electricity, and the system can draw a small amount of heated or cooled air. Ohio requires every mitigation proposal to include an estimate of the annual operating cost, so you see the number before signing.
More detail
The EPA's guidance is plain: fan-powered systems are the most effective option and slightly increase the electric bill, by an amount that depends on the climate, the system, and the house. In a zone 5A Central Ohio winter the bigger variable is heat loss, and the sealing done during the install (floor-wall joint, cracks, the sump cover) limits how much warm basement air the fan can pull down through the slab. You can check the fan's draw yourself from the rating on its housing and your AEP Ohio rate. Never switch the fan off to save money; the EPA is explicit that it must run continuously for the system to work. If the operating estimate on a proposal looks high or oddly low, ask how it was calculated and which fan it assumes.