You will get no better fuel ecomony. Lets get that one clear. You still have to deliver the same energy with drive to 2 or 4 wheels to get the same amount of mass to move. The transfer case with send it either one way (rear) or two ways (rear and front) and you'd be hard pressed to 'quantify' any changes in mechanical losses that can be easily measured.
I disagree with this. Technically.
I don't think you'll see any noticeable improvement when driving around town, since you're consuming so much energy bringing a 5k - 6k pound vehicle up to speed repeatedly.
In long highway driving, you'll see an improvement. You're cutting out the energy losses of the entire front half of the drivetrain. The only losses you're left with are from the wheel bearings and seals. With the standard US-market setup, you're spinning two u-joints, at least three bearings in the differential, the differential gears themselves, plus churning that Birfield butter and balls. Plus the front output of the transfer case. That's got to be at least something like a 5 - 10% efficiency loss.
Introduction on how to calculate drivetrain (driveline) losses and their impact on the overall efficiency of the vehicle
x-engineer.org
That said, if you're concerned about highway mileage, then you're probably in the wrong vehicle. Unless you're somewhere like Australia, where enthusiasts regularly drive very long distances on dry, paved roads just to begin their off-road adventure.
So, again, there are some very specific benefits to a part-time conversion, but chances are that if you're reading this they don't apply to you.
If a part time conversion saves you a 10% energy loss, and if the part time kit costs you $350, then at $5 per gallon it will take 700 gallons to break even. If gas were $3/gal (approximate 2018 peak), it would take 1,167 gallons to break even.