Thank y0u both!
This seems to be the relevant section, at the very end:
A serological test is advantageous because it can detect antibodies even if a patient has recovered, whereas a PCR test can detect the virus only if the person is currently sick. However, both tests might miss cases if samples are taken too early, when the viral load is too low or if the person's body hasn't produced antibodies against the virus yet, Adalja said.
For the serologic test, it can take about a week before the body produces ample antibodies, although "as we get more serologic tests, there will be guidance on what timeframes are needed to do a serologic test on [COVID-19]," Adalja said.
BBM
So it seems that we just don’t know yet. What prompted my question was when a reporter asked VP Pence if the President had been tested (because of his contact with Collins and Gaetz wh0 were exposed). It seemed to me to be a little soon to test him, and later this evening the answer was “No.”