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Yes, false negatives for covid-19 testing is high.

"A recent study in the Annals of Internal Medicine from researchers at Johns Hopkins University in Baltimore found the effectiveness of RT-PCR tests, the most common type of test for the coronavirus globally, varies dramatically over the course of COVID-19 infection.

"In the first few days before symptoms typically show up, researchers found, the chance of getting a false negative result ranged from 100 per cent on Day 1 to 67 per cent on Day 4.

"After symptoms began to show, false negative results fell to 38 per cent on Day 5 and to 20 per cent on Day 8 – but rose again everyday after that.

"That means at best, COVID-19 patients were found to have a one in five chance of getting a negative test result during their infection even if they were actually positive."

https://www.cbc.ca/news/health/coronavirus-test-false-negative-1.5610114