I can say through listening to a huge number of car amps that it's a definite yes but with car amps it's easy to explain why. This may apply to any amp but there's always some distortion from clipping, even if it's not showing up on tests as a clip (since tests are conducted using pure tones, not complex analog audio signals) but will always be there in some form. That tiny clip is hidden within the sound and it may shine through at different levels (but not loud enough for our brains to pinpoint it as an added noise) and in different octaves depending on the amps design and components used.
I think a good test, since it was stated that amps and receivers sold at different price points may very well have been made using the exact same boards but we're assembled at different locations using slightly different parts. Then they fudge ratings and add a feature to make the next higher prices model.
Using the same boards and different parts should be able to provide a way more realistic approach of comparing. Since you can actually say that the only difference are the parts used. This way you will have a control that you know for sure and can say as a fact that it does or doesn't matter or it can affect sound to a degree but it won't be the only thing that may be affecting it. I can't see any other way to start ruling out things based on actual known differences. Even finding the same exact models and testing between different locations of assembly or revisions should reveal some sonic difference if it's true. If it's imperceptible, then you can toss out the components being a large issue and look at the design of the amps next and so on.
When you aren't even sure if amps sound different how can you try and find out why it is? Without physically making changes between identical amps (as an obvious starting point) or have the ability to do tests using complex analog signals in a direct overlay of signal input to output I dont see how it:s possible to even get started on why!
1 more thing, you can't test an amp that has a damping factor of 100 to an amp with over 500 and expect them to sound the same. I know very well how awful any Panasonic digital amp sounds and I doubt they will even have a similar sinad rating. This again is coming down to when the silent clip starts to become unnoticably injected into the overall sound.
I'm willing to bet there's always a clip that's hidden in complex signal amplification to some degree, some amps just hold that clip to a minimum while others reveal it at certain output levels. You just cannot say that an amp isn't clipping unless you can measure a complex analog signal at any exact moment in time as it compares to the input signal at that exact moment it leaves the amp. I don't see how else you can test an amp, this is why the only specs I consider important are power (watts) into a 1 ohm load compared to 8 ohms (stability in current) and damping factor. Those will tell you more about the amp than signal to noise (which has become a mute (pun intended) point in today's world) or total watt output since fluctuations in complex signals are going to be where an amp gets stressed and clipping will be introduced, even with large overhead there still can be hidden clips at different frequencies.
So yes, all amps sound different, but it's not changing the signal by loss or inaccurate reproduction it's the amount of clipping and at what frequency the clip occurs, So caps may play a big part of why the clip occurs but also the board trace power handling might be a big factor restricting the path or even the solder used could be a factor not considered. 1000 solder joints add up.