If they are minis, then no they could not be registered as grade or NOA with ADGA. Grade or NOA are for each of the standard breeds: Nubian, LaMancha, Alpine, etc. ADGA within the last 2 years I think added Nigerian Dwarfs and they only register Purebred Nigerians. There is no Grade or experimental herdbook for Nigerians right now.. I don't know if they are planning on changing that, but right now it is not that way. So if you had a MiniNubian it could not be registered with ADGA, even though it would have Nigerian in it. And of course, ADGA shows require the goats to be ADGA registered.
Hope that helps . If you have more questions let me know.
Hornless, it works that way if they are double-registered.. maybe that is what you are thinking of. If a goat is AGS registered it can also sometimes be ADGA registered (and I think it is pretty easy to do but I have never done it, so I am not certain). But no, you can't just show an AGS registered goat in an ADGA show. It has to be registered with the registry.