This already happened in Seattle [1]. Undetected COVID deaths are not "unexplained" because they look like flu deaths, so they're simply catalogued as being from the flu.
"In fact, officials would later discover through testing, the virus had already contributed to the deaths of two people, and it would go on to kill 20 more in the Seattle region over the following days."
[1] https://www.nytimes.com/2020/03/10/us/coronavirus-testing-de...
"In fact, officials would later discover through testing, the virus had already contributed to the deaths of two people, and it would go on to kill 20 more in the Seattle region over the following days." [1] https://www.nytimes.com/2020/03/10/us/coronavirus-testing-de...