The torque convertor shouldn’t lock up in third gear, but I know some vehicles are programed different than others. Try running around in third gear without a load on the truck and watch your tach & listen. The torque convertor is most apt to lock under light engine loads. If it does lock then, you’ll know for sure.
It depends on the terrain, but in my experience you’re tranny is going to do a whole lot more shifting up and down if you try to use overdrive. I’ve spent many hours pulling trailers on the interstate in 3rd gear and haven’t seen one indication of it hurting a thing.
FYI - When I first bought my ‘05 Silverado with 95,000 miles, the torque convertor would not stay locked in until I got over 60 mph. At a constant 50 mph you could see the tach go up and down as the TC locked and unlocked. My brother-in-law fixed this problem by shimming the springs on the valve that controls TC lock-up with a couple 1/4 inch ball bearings. Evidently it’s a common problem with the 4L60 transmissions. Sure was a bunch cheaper than what a shop would have charged me to rebuild the transmission!