As far as I can tell, the other archive formats are not supported. I am not sure why one would want to use these archives as module resources or how it would work; however, I thought I would try it and report my findings.
As a test, I added an EAR as a module resource, added a dependency to the module in the jboss-deployment-structure.xml of an application with a dependency on libraries that were in the EAR, and then executed the code in the application that depends on the libraries in the EAR. This resulted in class not found issues.
Based on my testing, I will assume that the answer to my original question is that archive formats besides JAR are not supported for module resources.