According to the documentation, restoring of a 6.x backup to a later version of teamcity is possible.
I have production server running 6.5.4 (build 18046).
I have a mirror server with 7.0.3 installed.
command line to restore database was:
"maintainDB.cmd restore -F F:\TeamCity\.BuildServer\backup\TeamCity_Backup_20120701_230000.zip -A F:\TeamCity\.BuildServer -T F:\TeamCity\ConfigBackup\database.properties"
This restored to a new database instance with no errors. After restoring the backup to a new database with maintainDB, I receive the following error on startup of the TeamCity web server:
"Data format between data directory and the database does not match: configuration version is 514 but database version is 454.
This probably means you changed TeamCity data directory or database in an inconsistent way.
Both database and data directory should be in a consistent state and upgraded at the same time. Please reconfigure the settings or restore the data from backup and restart TeamCity server. ".