I have not taken NRA Basic Shotgun, but I did take NRA Basic Pistol. My guess is that the curriculum would be similar: safe handling, stance, grip, loading/unloading, and marksmanship. It gets students oriented to shooting as a recreational or competitive activity, but it is by no means a defensive or tactical course.
To the best of my knowledge, the NRA does not offer a defensive or tactical course for shotgun. However, there are plenty of other organizations/schools that do.