Yes, you can update the computer settings to account for different size tires and thus a different count of rotations per mile. There are many programmers available to consumers that allow us to update the computer settings ourselves but the dealer can also update the settings for you. Buying a programmer will cost you $300 to $500 depending on which you get.
On the '14 and up, if you take the vehicle to a dealer for service, GM can see that you've updated the programming and could void all or part of your warranty depending on what settings you changed if they contributed to a failure of some kind. On the older vehicles, if you reset to factory settings before taking it to a dealer for service, they couldn't tell you'd done anything to it.
The local dealer to me it would be a bout $50 to $60 for the shop time to have them re-program my truck for a different tire size and any dealer would be far less likely to squawk about the warranty because it was just tire size and a dealer did the work.
I'd fight tooth and nail if they tried to void my warranty because I adjusted tire size settings myself but, at the same time, paying them $60 vs. spending $400 for a programming is fine by me. Once my warranty is up, I'll get a programmer and tune the motor, remove speed limiter, etc. but on a new model year vehicle and with some of the issues others have seen, I'll avoid risking warranty coverage!
As for mileage, a larger tire, and particularly a heavier 10 ply LT tire vs. the 4 ply P rated stock tires, means more rotating mass and therefor more power/fuel required to get move the vehicle. This is generally why there's a fuel economy loss when going with larger tires.
That being said, my '03 had 4.10 gearing and going with a 285/75R16 actually yielded better mileage than the stock 265/75R16 because my motor was at a lower RPM for the same speed and therefor using less fuel per mile.