I don't see why you would have a problem. I might not be aware of a caveat out there, but depending on the version of CCM on the MCS7815, you should be able to do a backup and restore.
The question at hand is what version of CCM are you backing from and what version are you restoring to.
Please read this:
http://ftp.cisco.com/cisco/crypto/3DES/voice/cmva/MCSbackup.3-5-53-UserGuide.pdf
Cisco IP Telephony Applications Backup Utility 3.5.52 supports the following Cisco CallManager
releases, which serve as minimum requirements:
Cisco CallManager 3.3(3) or earlier
All releases of Cisco CallManager 3.2
All releases of Cisco CallManager 3.1
All releases of Cisco CallManager 3.0
There is also a backup software for CCM 4.
H. M.