Peter,
To the extent that protection circuitry often includes some type of current limiting that reduces the output power the amplifier will produce, and hence cause it to go into clipping much sooner than would otherwise occur, then yes, amplifiers can indeed sound different.
I'm often misquoted regarding statements I've made about the "sound" of amplifiers, both here in the forums and in various magazine articles over the years. There are numerous reasons why amplifiers may sound different, especially when they are driven to their output limits. However, to reiterate, when solid-state amplifiers have ruler-flat frequency response (most do), distortion levels below, say, 0.2%, and are free from design errors that may compromise one or more aspects of performance (e.g. many early solid-state designs, mostly Japanese, used huge amounts of negative feedback to reduce THD distortion to 0.0002% or less), and when they are not driven at or near the limits of their output capabilities, they will tend to sound identical. At least, that is my experience participating in double-blind comparisons of a variety of different solid-state amplifiers. I certainly have not heard every amplifier, and would be reluctant to generalize to newer designs that were never part of the tests I participated in.
Just in passing, I'll comment that swapping cables trying to detect the nuances of amplifier sound differences takes too much time. Ideally, the switching should be instantaneous with relay-operated switching, or certainly take no longer than about 3 seconds, and of course it should be done blind.
Regards,
Alan
