And next, when we use the term quiet or noisy are we talking solely about the hiss in the speaker drivers ?
A noisy tube will be just that. It will raise the noise floor through your system. IOW, where your system once had a black background, there is now a layer of noise. In a worst case scenario you will hear some tube rush through the speakers.
Amps, preamps, phonostages with high gain will make the noise from a tube more audible. A phonostage with it’s high amount of gain should always use tubes that have been noise-tested.
Even true NOS tubes in original boxes can have a degree of noise.