NBU Media server Deduplication

hi,

I have  one master server and two NBU appliances with dedupe pools as Media server. if server DBSvr1 is configured to backup to appliance A dedupe pool, and configured to backup to appliance B's dedupe pool on the following week. does the only unique data be stored in appliance B's dedupe pool? Meaning    is the data globally deduped within a backup domain/

Thank you