Sure, the previous decent sized company (~1000+ devs) had that exact metric available.
Visits to the status page generally that is. Now whether you could actually correlate that to an increase in errors for a particular component, no so much ;)
I'm sure it's totally feasible but it requires a certain amount of discipline to have consistency in logging/metric standards across all your applications to some extent.
Even worse, some applications would return a shared error page but internally, I believe it was logged as a 301 redirect until someone spotted it :)