I experimented with this before on my Ram. With the T/H button on the shifts are crisper, hold each gear longer and locks out overdrive, so I am usually cruising around 2K RPM. I found slightly more gas is used with it on the whole time especially on long interstate drives.
But what I really noticed was the difference in transmission temps. With it off and gear hunting a lot, the temps eventually climb to quite a high level, not overheating, but warm. With the T/H button on it climbs to an acceptable level and stays there.
So while you might experience slightly more fuel consumed, I am sure you are saving wear on your tranny running it cooler. I leave mine on most of the time when towing after my experiment ;)