We have a large libraries that are shared amongst the distributed nodes, and some of those dist nodes share media pools without issue--providing you have all the latest patches.
In a properly configured SAN environment, the dist nodes will pull the tape library configuration, including the device groups, from the primary. When a backup (or any type of job) kicks off on a dist node, it requests a tape from the primary. The primary instructs the library to move the tape to a drive, reads/formats the tape, and passes it back to the dist node, and then the job begins.
If using a Central Database, you cannot have duplicate pool names.