Seems like they would as its a valid PCR test. You can fill the paperwork in nearly up to the last minute. Our flight was 7am on a Saturday and I filled out the portal paperwork at 11am the Friday before. So if you go the test done close to the 5 day window, you should have plenty of time. USVI accepts antigen tests as well though - pretty easy to get at many places. We did ours before our trip at CVS after PCR tests didn't come back in time. Technically they did, but showed up at midnight, 7 hours before our flight. Wasn't going to take that chance and it would have been stressful getting up for our flights and having to fill in the paperwork at that time as well.

Matt