Yes, that's the sort of thing you'd need to be doing in order to have any degree of certainty you weren't transmitting a cold virus. Obviously most humans don't live like this.
Not sure how reliable the data on transmission of the common cold is, since we test so infrequently. Covid is an unusual virus in that respect, because most of them don't have a bloc of people testing with no symptoms. Even with flu it's easier than colds because people test somewhat more often for that, albeit nothing like as much as covid. And there are some wildly varying figures out there for how much flu is asymptomatic.
It's also not really comparing like with like. We use a cold colloquially to mean a substantial range of viruses, whereas covid 19 is just the one. I'm not a fan of defining covid in relation to colds in general.