First off, This is a Chevy and not a Ford so you're not hitting an "overdrive" button on the end of the shifter - it's the "tow/haul mode" button if just clicked once quickly. And No, it won't change your RPM's because all it does is change the shift points between gears as you accelerate and run up through them to finally arrive at overdrive.
If you really want to disable your overdrive, press and HOLD the tow/haul button - but be prepared to see a sharp rise in RPM's when you do (I don't suggest doing at highway speeds). At that point you should also see a light on your dash with OD and a line through it indicating that the overdrive is disabled.
I can't say if 2200 rpm is too high or just right - my Silverado is a 2500HD with the Duramax and Allison so what I get won't be comparable to what you should get. However, I get 500 miles on a complete 26 gallon tank of diesel - or I did before I went to larger tires. I have a speedo error now and haven't remeasured it. There are three things to check when you see mileage like yours: 1) a basic tune up with plugs, air filter, fuel filter, pcv valve, etc. 2) make sure your torque converter is locking up at highway speeds; and 3) check your rear axle ratio. If you have a 4.10:1 rear axle for towing then you are getting the mileage I would expect to see. But if you have a 3.73 or lower ratio then you've got an issue here.
To check if you torque converter is locking up properly, you can drive along at a steady 50mph on flat terrain (the converter should be locked up at this point). With your right foot still on the gas, use your left foot and lightly press your brake pedal - not firm enough to slow you down but just enough to activate the brake lights. You should see a 200-300 jump in RPM indicating that the converter is unlocking. If you don't see the jump then it may not be locked up to begin with.
Cheers - Jonathan