I think in that case you will lost the failover capability.
This is a classic description of a network partition (split brain) scenario.
JBM 1.x does not have any specific code for preventing split brain from occurring. For JBM 1.x we recommend mitigating this by e.g. using IP bonding to reduce the probability of this occurring.
If it does occur, duplicate delivery of messages is possible. If this is a major problem in the application, we recommend the user implements application level duplicate detection to weed out any duplicates.
JBM 2.0 will have "split brain" detection. This has been discussed on JIRA and on the forums.