Speed to market would not be the issue, but the speed of the test could be. PCR tests, which take days to get the results are very accurate. Immunoassays which look at the blood for antibodies are less so. There is more variability in the antibodies than the virus. Whether the variability results in false positive or false negative may depend on the uniqueness of the antigen it is targeting.
https://www.nature.com/articles/d41587-020-00010-2