Can paraneoplastic panel (through mayo clinic) be false negative results?

Difficult matter. This test is only useful when it is Abnormal. But it does not help at all when it is normal panel(which means there is no abnormaility found but it does not exclude any diagnosis because there is nothing predictable about a paraneoplastic panel). So you can not say it is false negative . it is designed to be useful only if it shows an abnormality that supports a clinical diagnosis of cancer .