There have been some studies that have looked at that, and there are certainly some studies now looking at patients who were infected with the original SARS, so SARS-CoV-1. Again, in those studies the immunity lasts really only for two to three years, so even though there are potentially some low levels of protection, coronaviruses don't generate historically long-lasting protection.
Children have a very high natural immunity. Their immune system is often quite active, whereas that wanes as they get older, so part of the reason children and young adults aren't getting as severely ill could be that they have the most robust and natural or innate immune response.