I disagree...
There's the varnish production stage, which will take place immediately in places, and in tiny quantities. It's slowed by anti-oxidants, but not stopped.
It build up in the oil, being dispersed in the oil...hotter oil holds more, colder oil holds less...that's why it plates out in places like rocker covers and turbine steam valve control gear. It gets dissolved in the hot parts, and dropped
When the oil, even hot cannot hold the products, then it's runaway.
Even at this end stage, in heavy equipment, the oil still lubricates, but there's risk of losing control of where and how much it goes.
So I disagree...until you get to the runaway stage...but the oil is shagged by that point, not in the least because of it's varnish potential.