According to the spec (see below excerpt of ejb3.2 specification) the application should not avaialble if a Singleton initialization has failed.

The current behaviour with two ejb.jar's in one ear, or other combinations is
that the failure is logged, the deployment seems removed (there is a APP.ear.failed marker file) but another EJB of a second jar inside the ear is accesible, also web applications war deployemts are started.

from the Spec 3.2

4.8.1 Singleton Session Bean Initialization
By default, the container is responsible for deciding when to initialize a singleton session bean instance.
However, the Bean Provider can optionally configure the singleton session bean for eager initialization.
If the Startup annotation appears on the singleton session bean class or if the singleton session bean
has been designated via the deployment descriptor as requiring eager initialization, the container must
initialize the singleton session bean instance during the application startup sequence.

• • • • • The container must initialize all such startup-time singleton session beans before any external client requests (that is,
          client requests originating outside of the application) are delivered to any enterprise bean components in
          the application. ******

4.8.4 Singleton SB error handling
Errors occurring during singleton session bean initialization are considered fatal and must result in the
discarding of the singleton session bean instance. ...
If a singleton session bean fails to initialize, attempted invocations on the singleton session bean result in the
javax.ejb.NoSuchEJBException exception as defined by Section 3.4.3 and Section 3.4.4 .