Can this function be used to generate the texture coordinates of any model?
If you’re asking if it will do the work of UV-mapping tools then no.
Texture coordinate generation is usefull for special effects like fog, reflections or shadow mapping. It’s also usefull for covering landscape with textures, creating water or sky.
Another example would be volume rendering.
You can use it to texture a model, but it will probably require using it multiple times for diffeent parts of model.