This has already been asked on Meta SE, and it looks like the current answer remains 'no', but I do think it'd be nice to be able to assign a correct answer to questions which have hit a certain age and likely will never be revisited by the original question asker. While the votes do help discern the best community answer, it is a little annoying to not have the right answer accepted for something like Dissolve in ArcMap gives ERROR 999999 which is clearly answered but is unlikley to ever be accepted.
Across sites, it sounds like the 'accepted' answer means one thing: the author has checked the box.
Within this site, it seems like we're moving toward a social shaming approach for those questioners who do not accept any answers to their questions, which is sufficient for enforcing this kind of policy without any software changes.