Can I do the following in theory?
Is this the normal thing?

Use an app server like JBoss or Weblogic.

Have a stateless session bean that implements the facade pattern and uses Container Managed Transactions.

Have a domain object model represented by "hibernate" java classes.

From my session bean, either call my hibernate java classes and/or call some custom SQL (say for performance reasons). Having everything under the CM transaction which is demarcated by my session bean method.

This is perfectly possible and very common, too.