You can mix and match certification agencies for OW, AOW, Nitrox, ect. The prerequisites will say "AOW or equivalent from another agency" as an example. As far as PADI's Nitrox course, there were no dives and since I recently bought a computer, I did the computer version of the class. There is a tables version that will make you figure MOD's, EAD's and so on. The requirements were to analyze a couple tanks, and plan a 2 tank repetitive dive to various depths. You would have to show competency in programing the computer you would be using or be able to perform the dive using tables. You did not have to make dives. I don't feel you would learn anything more if you were to make the dives or not. Breathing off a tank is the same with either air or nitrox in them. Granted, you have to know what your max depth is for the mix and be sure not to exceed it...
As far as NAUI goes, I know they make you do the dives. I would have wanted to make the dives for my PADI cert just to get the dive experience, but that was hundreds of dives ago. I like to combine Nitrox with AOW that way you get dives in either way with the PADI cert.