I created a test project with an EJB module, a WAR module and an EAR module. The WAR module has an endpoint with an injection point:

@Inject private MyInjectable injectable;

I have a producer for this in the EJB module:

@ApplicationScoped public class MyProducer {
  @Produces MyInjectable getMyInjectable() { return new MyInjectable(); }
}

Finally, I added an extension that does nothing but listen to ProcessAnnotatedType. My CDI extension reference is this: https://docs.jboss.org/weld/reference/latest/en-US/html/extend.html

The application fails to start:

Caused by: org.jboss.weld.exceptions.DeploymentException: WELD-001408: Unsatisfied dependencies for type MyInjectable with qualifiers @Default
  at injection point [BackedAnnotatedField] @Inject private test.MyEndpoint.injectable
  at test.MyEndpoint.injectable(MyEndpoint.java:0)

If I rename my-ejb/src/main/resources/services to services.bak, and comment out the implements Extension in the MyExtension class, it starts up fine. It seems adding the extension to the EJB causes Weld to not process the producer methods (see startup.log).