I have texture applied in the UV editor (that's what I always do, because I need to see it in the viewport) and I have material applied because that is a requirement of IQM exporter.
If someone would ever write about md3shader in the docs or ReadMe, I would probably have that
So, no, I don't have that and I am not even sure where to set that and how.
I never applied anything with the name NULL to the mesh.
There is a good model viewer called Noesis, it loads MD3, but it seems like there is no UV map nor there is a shader/texture. It's just a mesh.