If the dealer gives you any grief about larger than OE tires (within reason) then find another dealer. I had a dealer look at my truck and told me they won't even try to diagnose my axle seal leak under warranty because I had a 2" leveling kit on it. The next dealer gladly took care of the issue, under warranty, without batting an eye. Every dealer is different in their acceptance of aftermarket parts.
That's kind of what I was thinking- really depends on the dealer. My dealership seems pretty fair and reasonable. They took good care of me when I had the torque converter issue, so I'd be shocked if they raised a stink about tire size (especially a minimal size increase).
2017 Chevy Colorado CCSB Z71 4x4 - Zone 1.25" Level - 265/70/17 Falken Wildpeak AT3W