If you have a positive test you still have to stay in for seven days but they don't tell you why since the argument for the non-tested should also apply to the ones with a positive test.
However there is no hard data here but I think these anti-body tests are better for statistics than prevention. Maybe you could even get a "corona passport" so that when you have had it and become immune you have more freedom.
[1] https://www.fhi.no/nettpub/coronavirus/rad-til-personer-som-... (Norwegian)