No, it's not possible. The database is embedded and cannot be decoupled from the server itself, this is by design. Also it makes little sense, the majority of the database is taken by flat files, not by a DB so moving a small piece outside of NBU won't make any difference.
Many years ago it was possible to have a separate EMM server but it was such a messy configuration that nobody really used it hence it was removed.
Thanks for the update.
The objective was to introduce some HA into the DB, other than having a clustered IaaS instance in the cloud. Can these flat files not be shared?
Is there any future changes for this to be made possible?
The HA options for a non-clustered master server are described in this this doc:
NetBackup in Highly Available Environments Administrator's Guide
For 'future' options, you need to get hold of Product Management via your local Veritas office.