My question is will I be losing some kind of quality by dithering down to 16bit in Audacity as compared to using the built-in UV22 dithering on the AD-1000. Is it really the same process or not at all?
You might see gains or losses. I believe that UV22 is considered a good dithering algorithm, what Audacity uses I am not sure of. In post you do have a lot of choices though, I believe r8brain (found for free from voxengo, alas only windows) is a respected choice.
You would definitely gain a lot more than any loss if going more than 16 bits allows you to adjust gain upwards in post. Going 16 bits, you get what you have including all safety margin on volume. Using the extra bits allows you to continue having a safety margin when recording, raising volumes afterwards and still not increase the noise floor level.
Still, a lot of these things are totally swamped by the decisions you make on location on choice of mics and positioning of them. I would not spend too much thought on them, or as the Nike slogan used to say, just do it.
// Gunnar