You're right, I did use a generalization.
CYA, once added, doesn't typically reduce except from splashout and backwashing and consequent refilling, which removes water and replaces it w/ fresh. There have been some occasions where pools have been opened in the spring after being closed all winter, where the CYA levels have gone down after the FC is depleted. It tends to be the exception, rather than the rule, and we aren't real sure as to why it happens, though there appears to be a bacteria involved in the process. So it happens, but one can't count on it.
Also, as a general rule, problems stemming from high CYA manifest themselves during the swim season, rather than over the winter, and the fix, if one is expecting a fix while actually able to USE the pool, is water replacement.