That depends on the vehicle and more specifically, the engine.
Changing gears puts the vehicle back in its designated power band. When choosing gears it shouldn't be random but should be done calculating the proper set. The larger tires change put our vehicles outside their power band. The size also causes more drag. Putting the vehicle back into its intended range may not be enough, sometimes you need to raise the RPM slightly to make up for drag. When I played with drag cars in my youth, you would calculate the gear ratio based on power band then calculate tire size to fine tune it.
Bottom line here is, gear ratio will help MPG by putting the vehicle back in its proper power range but, but can only help a little of the loss due to the extra weight we add and the extra drag from tires.
Another thing that needs consideration is pinion size and axle size. The lower the gear, the smaller the pinion and weaker the pinion gets. As you lower gears you also multiply torque. The larger tires strain axles as it is, adding more torque is fine as long as you don't over do it for the axle strength. The more splines an axle has, the larger the diameter and the stronger. To me, a 4.88-5.13 and a 37" tire are proper for most Jeeps and the limit for Dana 44's that are driven hard.
