If the old tires had severe uneven wear, they could have introduced some sideways pressure that would mess up the alignment readings. I doubt it would be enough to feel, but it might be enough to measure. On the other hand, if the tires were nice and flat even if bald, there shouldn't be anything to worry about.
Is the steering wheel centered? On a nice smooth road without a huge crown, does it track straight if you take your hands off the wheel? Does the truck go where you point it, or does it follow the grooves in the road -- are you always fighting it to stay in your lane? Does the steering return to center nicely after a turn? The answers to these questions will tell you whether or not you need another alignment.