Can noise add complexity or "warmth" to clipped signal?

[Aentons]

I watched this video about carbon comp resistor noise and it got me thinking:
[youtube width=480 height=640]https://www.youtube.com/watch?v=yWj5rQRM6Ls[/youtube]

Not quite sure how to word this but I'll try... The Hi-fi audio world is normally concerned with signal fidelity and we here on this forum tend to explore the world of signal distortion and its myriad forms. So with the exploratory and learning spirit in mind...

I'm curious about various ways of how purposely engineered noise (or distortion) on an audio signal could potentially make it sound different or more interesting or more "complex" but not necessarily with just odd/even harmonics. Take for instance, the use of carbon comp resistors in amps, or the preference of some to listen to vinyl, because they are warmer or softer or more pleasant or whatever. What are some ways one could exploit noise sources and mold them in new and interesting ways and not just "rolling off the highs"?

Could you do something like introduce white/pink noise within a feedback loop before/after normal soft clipping or tone shaping?
Noise could maybe come from:
- thermal noise from carbon comp resistor string(as shown in the video)
- low voltage avalanche diode in breakdown mode
- messing with opamp input offset voltage pins in some way?

[Aentons]

Noisy sine waves... These also inspired me to start thinking about this:
[youtube width=480 height=640]https://www.youtube.com/watch?v=SP3zTandUjA[/youtube]

[youtube width=480 height=640]https://www.youtube.com/watch?v=7GWUmEJNDng&t=559s[/youtube]