Netbackup Appliances - is Deduplication free?

You do not need to purchase a license for an appliance. Licensing is done for NetBackup with Traditional or Capacity based licensing and includes the dedplication feature (Capacity only). So if you're licensed for it, then you can use it with the appliance.
 

As per Riaan's excellent reply, Dedupe license is only free/included if you have Capactity (Platform Base – Complete Edition) license.

If traditional license, you need a tier 2 Enterprise server license for the appliance and NetBackup Data Protection Optimization Add-On.