As I said, the math says we can fully express any signal in either the time domain or the frequency domain so in that regard, yes it's all just amplitude, phase and frequency. That only works if I know the signal end-to-end before hand which we don't so, in the practical sense, the frequency measurements at any given time are an approximation and don't capture the dynamics (change in response with amplitude, history, or other conditions e.g. temp). I've heard some pretty good replications in solid state (Peavey Transtube is the one I've used) and all-digital emulations (Revalver) but I don't have much time playing on tube amps so I can't talk to how well they do -