I discoverd a link from someone on the forum with a similar question.
I found out that JBoss 2.4.4 has the ability to automatically deploy an unpackaged .ear file.
I tried this and it works. It doesn't completely answer my question since it requires me to unpackage my .war file instead of just dropping the .war file into the JBoss deploy directory.
In case anyone wants to know...
Create a new directory in the JBoss deploy directory and name it "<some name>.ear". Under this new directory create a directory called "META-INF". This directory is for placing your "application.xml" file.
Also under the "<some name>.ear" directory you create a directory with the same name as your .war file. Next unpackage your .war file into that new directory that has the same name. The last step is to register with the JBoss auto-deploy mechanism the .ear directory that you just created. This is done in the "jboss.jcml" file in the section called Auto Deployment. The edited section will look something like-
When you start up JBoss it should autodeploy the webapplication and you can access it using the name defined in the "application.xml" file.