I have a 2012 Lincoln MKZ Hybrid, which has the cooled seats standard.
From what I understand, the cooled seats are just a fan in the seat blowing from a "cool plate". Its the same fan that is used for the heated seats. There is no direct connection to the a/c. I believe the only additional fuel consumption would come from the tiny amount of power used to spin the fan in the seat. And unless they changed the system for the new style, I'm sure it'll be the same as what is in mine. I've noticed that the system works best when the a/c has already been running through the car and its essentially just a fan for the already cool cabin air to go through the seat bottom and back. You wont really feel anything for a while if the car was sitting in the hot sun, I find myself waiting about 3-4 mins after driving to turn the cooled seat on, seems to get the fullest effect.
Lately thanks to the cooler weather in FL, I find myself riding with the windows down, and whether I have the cooled seat on or off, I dont notice any difference in fuel economy.
One thing I did do, was on my last drive I looked at the "ACCS" bar on the EmPower screen, and I noticed that turning on or off the cooled seat had pretty much zero effect on it (it was maybe the same as turning on a light, if that), while turning on the a/c caused it to jump 3-4 bars.
Thats the best info I can give, hope it helps a little bit.