Dithering is simply introducing noise at low level, in order to conceal the high levels of distortion present in digital signals as they approach silence (typically at the end of the fade or reverb tail). If you listen to this at high levels (careful!) you will hear a 16bit audio recording break up into grainy distortion just before it disappears. After dithering, the signal will disappear into a soft noisy haze, which is considerably more pleasant, particularly if you like to listen to the ends of fades at very high volume!
So yes, I’d say your 16bit recording would benefit from dithering. Dithering isn’t important if you’re staying in the 24bit world, because the digital noise floor is so much lower.