I doubt whether this would work, because MS will very likely have introduced significant schema changes to the MailStore databases across major versions of MS Exchange. By all means test, and post back, but I wouldn't test it in production.
FYI - the DB SCL was updated a few days ago to state the v7.6.0.4 now supports MS Exchange 2013 CU7.
Exactly what service pack and/or roll-up are your two MS Exchange servers running?
Here's a thing... I believe (but anyone else please feel fre to correct/advise)... that even sometimes going from for example MS Exchange 2010 SPx to SPy will mean that one won't be able to restore any of the prior backups taken (whilst MS Exchange was at 2013 SPx) back in to MS Exchange which is now 2013 SPy - this is just an example, and I don't know this for sure.
What is clear, is that if this is true, then this is NOT a NetBackup issue, as all backup products will have this problem - because it is to do with the way that the MS Mailstore databases are structured - i.e. the database schemas, and the schema changes that MS may, or may not, implement from version to version of MS Exchange Server. The only way to confirm this for sure, would be to read the release notes for MS Exchange, and see if MS make clear statements regarding version to version inter-operability.
This whole situation kind of makes me want to edit the keyword in MS Exchange backup policies to capture the versions of both NetBackup Client and MS Exchange Server - so that it is possible to (at a later time) track which backups came from whichever versions, e.g. use a keyword in the backup policies:
XXXX_YYYY
...where XXXX could the the NetBackup verson, and YYYY could be the MS Exchange version, e.g.
NBU7602_EXCH2013SPxCUz
Are there any NetBackup MS Exchange gurus who can comment on this?