On my 2004 EXT, the transmission shifts to OD while the Tow/Haul is active.
As far as I can tell, the only difference is the shift points are moved to a higher RPM to better take better advantage of the engine's horsepower and torque ranges.
I have towed my 25' Party Barge that weighs 5K pounds with the trailer, fuel and gear at highway speeds for hundreds of miles in Tow/Haul overdrive.
As long as I am on fairly level highway with steady speed, the transmission runs in OD and the torque converter is locked up.
BUT, it doesn't take much of a change in the road's inclination for the transmission to drop back a gear.
While out on the open highway, I often set the Tow/Haul mode and cruise control and let the truck do it's thing.
If the transmission gets too shifty, I throttle manually to keep it from bouncing around too much.
My main concern is the transmission temperature.
My truck has a trans temp gauge in the cluster and the optional auxiliary transmission oil cooler installed.
I usually see the transmission temp run 10-20 degrees higher than when not towing, and this has not been an issue yet.
And I mostly only tow this rig during the heat of summer with the a/c running full blast.
Driving your truck in Tow/Haul mode and selecting Drive is not going to hurt a thing.
For me, gas mileage is a minor concern when towing.
I know it's going to be bad.