The only potential benefit would be the lack of water vapor in N2, compared to normal air. In other words, using N2 should be about the same as using dry air. This may cause the pressure to respond more predictably to temperature changes. I don't see how using N2 would increase mileage unless it is simply being run at higher pressures.

BTW, do the purge the air out of the tire before they fill it with N2? If not, only about 2/3 will be N2, the rest will still be air.