Of course its worth trying to off-road in a 2wd truck...
Off-road means a lot of different things to a lot of different people... not all off-road environments require a 4x4.
I remember the first time I went off-road, it was basically a dirt fire/maintenance road and at the time I thought it was "wild" haha. Yes I had a 4x4 but any stock 2wd truck could have easily accomplished the same. It was enough to jump start the obsession, but the trails, driver skill, and your comfort level is only going to go up from there.
2WD with a good driver can still take you a long way, just be realistic with what you want to accomplish, Have the appropriate recovery gear and go with a friend. Stay out of the rock gardens, stay off things that require a lot of articulation where you might start getting a rear tire off the ground (unless you have a rear locker)
Even with a 4x4 truck I sometimes spend a good deal of time in 2WD when on the trail. I like to see how far I can get in 2WD. I switch into 4 after I get stuck or to get me out of a situation. If its obvious I need 4wd I switch to 4wd before the obstacle.
Bottom line, try it, enjoy it, don't go too hard right out of the gate.