No.
Allow me to explain...
“Clean” tone simply means there isn’t much distortion.
Distortion happens on an amp when the amplifier runs out of headroom, and the signal “clips,” that is, the sine waves reach the maximum level the preamp section can handle, and the tops are clipped off and become square waves.
The more volume coming from the guitar (and any pedals you’re using), the sooner the amplifier clips. If you want to clean up the tone, turn down the volume knob on your guitar.
Also, turn down the gain (sometimes the gain is labeled “volume” on a clean channel, because they’re the same thing) on the clean channel and turn up the master volume. This reduces clipping in the front end of the amp (the preamplifier section), and you can compensate for the volume loss by turning up the master volume.
There is one caveat: some amps clean up a bit if you reduce the bass. You can do it with an EQ pedal, you can do it at the amp. Bass tends to push tubes harder than higher frequencies.
But in general, turning down the volume knob on the guitar will nearly always reduce distortion, as will turning down any gain control for the clean channel, and you can compensate for the volume loss with the master volume.
Back in the old days before there were master volume or channel switching amps, the good players controlled their amps from their guitars. Turning down the volume meant a cleaner tone, turning the volume on the guitar up, the amp got dirtier. I use single channel amps, and control the gain from the guitar myself (because I’m so old that they didn’t even have schools when I was a boy, so I can’t be “old school”
).