I've enabled the access log in JBoss. I see that it logs 404's, but will it log 503 errors as well?
Depends. If the error is caused because JBoss is not available (service is stopped), then the error is generated and logged by Apache (or the web server you are using) and nothing will be logged by JBoss. If the error is generated by JBoss, it will be logged by both JBoss and web server.