Drupal does indeed store logs in the database, in a table called 'watchdog'. One problem I've run into is that if a popular page generates a bunch of warnings, there ends up being a pretty heavy write load on this table. It doesn't help matters that it's usually a MyISAM table, which means that all these writes stack up when the table gets locked, say when Drupal wants to do prune old entries. I've seen this nearly exhaust all the available MySQL threads. I think there is a module that you can use to stop this behavior. Alternately you can alter the table to use the BLACKHOLE engine.
One thing the author didn't mention, is that Drupal's content search is really bad. In order to perform multiple keyword searches it ends up generating these massive queries that join tens of search index tables. These queries can kill the MySQL join optimizer which can ultimately bring your MySQL server down.
While this bug has been fixed, the search queries are still gnarly and slow. If you're planning on running a Drupal site with a lot of content you'll definitely want to investigate an alternate search system, perhaps using something like Sphinx or Lucene.