The problem is that there are other RNA viruses besides SARS-CoV-2, such as influenza, and depending when in the disease course the samples were taken, the amount of irrelevant RNA might exceed the amount of SARS-CoV-2 RNA by orders of magnitude
There is going to be tons of RNA in saliva from sources besides SARS-CoV-2 always. Bits of RNA are floating around everywhere. Yes, there is some minimum threshold of SARS-CoV-2 density at which the test will fail to detect it, but this should just scale up by a factor of N when pooling over N people. I don’t see why other RNA those people have will be a problem any more than the other sources of RNA in a single person are a problem for a non-pooled test.
There is going to be tons of RNA in saliva from sources besides SARS-CoV-2 always. Bits of RNA are floating around everywhere. Yes, there is some minimum threshold of SARS-CoV-2 density at which the test will fail to detect it, but this should just scale up by a factor of N when pooling over N people. I don’t see why other RNA those people have will be a problem any more than the other sources of RNA in a single person are a problem for a non-pooled test.