After reading an article about the subject from O\'Reilly, I wanted to ask Stack Overflow for their thoughts on the matter.
I'd say no, given that a fairly large percentage of server errors involve problems communicating with databases. If the database were on another machine, network connectivity would be another source of errors that couldn't be logged.
If I were to log server errors to a database, it would be critical to have a backup logger that wrote locally (to an event log or file or something) in case the database was unreachable.