Thanks
@Revan
Tests are being made by rtPCR, which looks for the virus' RNA. Hence no, if the infection has cleared you won't test positive.
I've heard of some IgG/IgM tests going around, but know little to nothing about them. This sort of test searches for antibodies and would, presumably, be able to tell if you have antibodies agains coronavirus. I expect these to become important in the future if they can tell the difference between who is already immune or not. It would be tremendous to know who had assymptomatic infection, and if research proves these people will be immune, imaginw the benefit. You'll have an increasingly large population that you know would be safe to go out and take the higher-risk jobs.