For the Student and Course objects, I removed the annotation that had been present in the code and the objects still appeared to function with POJO Cache.
My initial tests were done programmatically with JBoss Cache running outside the JBoss server. I thought that might be the reason, I didn't need to aspectize the objects. So I deployed a test on a running JBoss server. And I got same results. The objects I attached to the POJO Cache were not aspectized nor were they Serializable and yet POJO Cache ran without error on a local instance. Maybe this is only true for Windows? And only locally. It probably doesn't work if replication is needed.