This bug is reported as upstream WILD FLY jira.
The functionality of JDBC Object store for transaction manager was added to EAP 6.1 as technical preview.
This bugzilla works for tracking the backport of this functionality.
I'm putting this bugzilla to Carlo because he should be responsible for backport. 
This bugzilla could be later canceled when it will be decided that the fix won't be put to EAP 6.1.1. 

In case that you configure transactions subsystem for running with JDBCObject store the app server fails to start because of (it seems so) a circular dependency.

You can expect the exception like:
ERROR [org.jboss.as.controller.management-operation] (ServerService Thread Pool -- 52) JBAS014612: Operation ("add") failed - address: ([("subsystem" => "transactions")]): org.jboss.msc.service.CircularDependencyException: Container jboss-as has a circular dependency: [service jboss.txn.ArjunaObjectStoreEnvironment, service jboss.txn.ArjunaRecoveryManager, service jboss.connector.transactionintegration, service jboss.cached-connection-manager, service jboss.data-source.java:jboss/datasources/JDBCObjectDS] 

My assumption came from the configuration similar to this:
<datasource jta="false" jndi-name="java:jboss/datasources/JDBCObjectDS" pool-name="JDBCObjectDS" enabled="true" use-ccm="false"> 
<connection-url>jdbc:postgresql://postgresserver.com:5432/user1</connection-url>
  <driver-class>org.postgresql.Driver</driver-class>
  <driver>postgresql-9.2-1002.jdbc4.jar</driver>
  <security>
    <user-name>user1</user-name>
    <password>user1</password>
  </security>
</datasource> 

and the transaction config looks like this
<jdbc-store datasource-jndi-name="java:jboss/datasources/JDBCObjectDS" />