Yes, but if you wanted to recreate everything you have to account for the frequency response at multiple loads and the HD at different levels, rectifier sag, transformer effects, etc.
In a way, it is like the digital simulation of a piano. That’s easier than the simulation of a tube amp, but it’s still not trivial. (Look at something like the Roland V-Piano versus the way that everyone just uses wavetable synthesis+recorded samples).
Everything that end up creating the piano sound is trivially measurable but the actual measurements you need to perform to develop the model are not.