Lots of good info on here... hopefully I can add a little more and tie it all up with a nice bow:
DEF does not in and of itself improve gas mileage.
What it does do is allow the truck to be tuned to run leaner vs a non DEF truck. Running lean leads to higher engine temperatures and pressures, which is good for power and efficiency, but produces NOX. DEF is used to break down the NOX in the exhaust. Another benefit of running lean is that virtually all injected fuel is burnt, so there is little soot remaining. This means that what would have ended up as soot in the DPF requiring regens, is instead burnt in the cylinder allowing you to go down the road.
On a non DEF cummins the engine runs rich, especially when the EGR activates. This is to slow down combustion and reduce the amount of NOX produced. Because combustion is slowed more soot is produced.
Water methanol injection can also be used to reduce nox. Water methanol injection is primarily used to increase the performance of an engine, by cooling the charge and allowing more aggressive timing (injection and/or ignition depending if we are talking gas or diesel). The added bonus of cooling the intake are charge, other than causing the engine to go leaner, is that a portion of the heat produced by the burning diesel is absorbed transforming the water mixture into steam. This means that combustion takes place just as violently (good for power), more completely due to the leaning of the fuel air mixture due to increases in density of the intake charge (good for power and reducing soot production) and at lower temperatures (reduces NOX output).
SO... if you have DEF, your engine can run leaner, which means you are not going to be relying on your egr as much to richen the mixture. Because you are not running an artificially rich mixture your engine burns all the fuel, leading it to turn this fuel into power to spin your wheels instead ofsoot clogging up your DPF, where it will need to be burnt out wasting more fuel. Running water meth theoretically reduces the workload of the DEF (depending how the monitoring sensors are hooked up), further reducing the need for the EGR, and consequently the DPF.
Unfortunately there are no factory installed water meth systems that I am aware of. Talk to Snow or AEM. They appear to be the big dogs ATM.