On its own, such a test has limited value. At best it can tell if someone is, or has been, infected with Covid-19. Additional tests are required to increase its usefulness, and it's the lack of molecular tests that creates a problem. Also, without being used in a good methodical data-gathering effort, there is limited usefulness for the larger population (e.g. in determining when it becomes acceptable to risk going back to work).
First test results do suggest that people may be immune to reinfection, but it's still too earlier to be very sure. Currently there are also tests being done to establish the differences in (re-)contamination risk between people with only mild or more servere sympthoms. That includes specific effects from children compared to adults.
The blood tests rely on the presence of antibodies which do not present immediately upon infection. The gene tests from nasal and throat swabs are still the gold standard there. There has been a lot of progress automating those tests and several companies that manufacture gene auto-analyzers have tests now. Abbott Labs in the US hopes to be sending out 1 million tests kits a week that run on their machines and there are others who are also ramping up production. These machines are mainly in hospital settings where point of care diagnoses is most important.
I've seen a couple of pin prick blood tests now but don't know what the ramp up for production is. These kinds of tests can be administered in a doctor's office and conceivably at home much the same way diabetics test their blood sugar levels with a pin prick (though that has largely been superseded by some new technologies). Blood tests can be more widely deployed than the gene tests and will be useful in getting good background numbers on the total number infected.