So, if somebody were sick in the past and recovered, then an RT-PCR test should show negative. Right?
In other words, the big increase in testing will only reveal currently-infected people and whether they had the disease in the past is irrelevant.
Again, generally correct.
A recovered patient is defined as recovered via 2 consecutive negative PCR tests 24 hrs apart. If those are the test results, Negative is the declaration. It takes more than 1 negative to be told to leave quarantine. Note this is only if there was a previous Positive.
A person that walks in with zero history and tests Negative is declared Negative. Only if Positive before that does it require 2 Negatives.
There are cases on record, not many but definitely not absurdly rare, where a Recovered patient leaves quarantine and is tested again a few weeks later and is Positive. The hope is he did not get re-infected. There is hope the swab is picking up viral segments from the original infection and not an active virus.
But . . . there are a few such cases that presented with symptoms. Those suggested re-infection and that’s very bad. It means immunity was short longevity.