If the component is an EJB, then, there shouldn't be a problem injecting an EM.
But....In JBoss 5, the JAX-RS integration isn't great. If you have an EJB, you cannot use scanning and you must manually list in the context-param resteasy.jndi.resource. If you still have scanning on, Resteasy will scan for the resource class and register it as a vanilla JAX-RS service and handle the lifecycle.
This is probably the problem.