Let me answer the main question first before I address the finer points: yes you can provide your own logging if you want.
I do want to point out that you are incorrect about a couple points. First, the JBoss LogManager isn't so much based on JUL as it completely replaces it. As it does replace log4j and provide implementations for slf4j and so on. It does in fact support MDC, via the slf4j or log4j or jboss-logging APIs. And it does in fact allow the usage of log4j appenders to be configured. The basic idea is that no matter which log API you use or how you use it, all the logs are handled consistently. This is why we replace JUL's log manager implementation - it's the only way to consistently and correctly merge JUL logs with log4j-style logs.
That said it does not presently have complete support for per-deployment logging configurations, though that is forthcoming in a (not too distant) future release.
Anyway, assuming you still want to go ahead with using your own logging API and implementation, you may also have to exclude "org.jboss.logging" in case you've got a secondary JAR linking against that.