What the question is really asking is whether or not you can install MSMQ on a cluster without a traditional shared disk and make use of the Majority Node Set (MNS) method of keeping disks in sync instead.
Looking at a selection of points from this clustering FAQ:
What is a Majority Node Set cluster?
It is a cluster that has a quorum based on local disks in each node, rather than a shared disk.
Can this method be used to replicate application data as well?
No, that is not possible in this version of clustering. Only Quorum information is replicated and maintained in a synchronized state by the clustering infrastructure.
How is the quorum information located on the system disk of each node kept in synch?
The server cluster infrastructure ensures that all changes are replicated and updated on all members in a cluster.
Does MNS get rid of the need for shared disks?
It depends on the application. For example, clustered SQL Server 2000 requires shared disk for data. Remember, MNS only removes the need for a shared disk quorum.
So, if you have an MNS cluster you will need a shared disk for MSMQ to access.