How much of a difference is either audible or measurable will depend on the design of the amp, how much internal cross-talk it demonstrates from channel to channel ( primarily due to poor circuit layout and / or internal cable routing ), the ability of the circuit to reject extraneous noises ( due to poor shielding and / or microphonics ), etc... These are all real factors that are both audible and measurable. Resistively shunting the input can only help this situation and lessen the potential for them to occur.
IF any of the above were to take place within the amp i.e. signals being induced into the early gain stages of an amp, it is the very nature of the circuit to not only amplify these signals, but to try to output them to a load. If there is no load, the output devices themselves and any loading circuitry inside the amp would have to absorb that energy and dissipate it as a slightly higher level of heat.
The level of heat and / or "abuse" that the output circuitry has to undergo in such cases is typically minimal with most well designed SS gear, but many circuits aren't "well designed" and / or built with quite as much precision as we would like to think. This goes for both inexpensive and quite costly products alike. Having said that, the mass majority of tubed gear should never be run without a load on it.
As such, using the approach that i mentioned above can only help the situation / put one's mind at ease / help the longevity of the gear / potentially improve sonics. NO, it is not "necessary" by any means and NOT following this procedure won't destroy your multi-channel amp beyond usability should you choose to not shunt the inputs and / or the outputs.
Having said that, i've always thought that the goals of most people frequenting this forum were to achieve the highest levels of performance from their gear / installation that they can. As such, i tried to provide some simple and reasonably inexpensive tips that i thought might apply to the subject at hand. Sorry if i offended anyone and / or presented my opinion as being anything other than my opinion. Sean
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