Stulax: Its an urban legend that has been around as long as AWD cars have been around, just like lowering the tailgate of a pickup. If you want the 5cent answer, IME the drivetrain losses are caused by the rotating masses, not by the viscous couplings and clutches that apply force to the front drive shaft. The only way to bypass these is to put unlocking hubs on the front wheels, a'la 1980s trucks. What would TRULY increase MPG is to gut the front AWD components of driveshaft, pumpkin, fluid, axles. This will eliminate their rotational inertia and reduce weight, which are both proven to increase efficiency.
As was mentioned above, the best way to increase MPG is by modifying your driving behaviour and maintaining your vehicle, including tire pressure and fluid changes.
The reason it is ill-advised, is that many cars rely on mechanical pumps to move lubrication within the drivetrain. When you disable any electronic controls systems you run the *risk* (I have not studied the pumpkins or xfer case on the FM platform) of reducing or eliminating lubrication causing unnecessary wear and tear.
If the possible gain is 0.1mpg, and the possible loss is a mechanical component in the $1000 neighborhood, why risk it? Do the easy things first. Heck removing the sound deadening will probably get you more than disabling the AWD system.