ADGA doesn't allow nigerian dwarf experimentals at this time so you can't register any non-registered nigerians or crosses yet.
A goat has to be registered with the registry the show is sactioned for...most of the time. I know they've had double sanctioned shows...but there was an issue awhile back about them...not sure if they do them anymore?
What breed association are you looking at? Yes, it matters when it comes to shows because some registries do a lot of shows (ADGA/AGS) and some registries don't do very many at all. There is another registry where you could register your goats. http://www.nmga.net/ I personally don't see any benefits in joining this registry besides having identification on your goats...other than that I don't know what it offers...maybe others could chime in about it?
The top registries right now for nigerian dwarfs are ADGA, AGS, and NDGA. They allow only purebred nigerians at this time.