Is it possible to restore a database backup chain taken from 3rd party backup tools and SQL Server? Example : Restoring A Full backup taken from 3rd party backup tools(Symantec or Red-Gate) using same tool + A Differential backup taken from SQL Server using SQL Server?
As long as the backups fit logically (they are taken in the correct order), it should be possible to do the restore. 3rd party tools just re-pack the backups in a different format (typically zipping them somehow), but present the internal data as a standard backup to SQL Server. As far as I know, they all use the APIs supplied by Microsoft to do their storage work. SQL Server doesn't care how the data is stored externally, as long as it gets it the right way when the restore takes place.
In short Yes. Caveat : I have only used RedGate SQL BackupPro RedGate provide a utility to convert a file into a native file type which you can use straight from SSMS without any SQL Backup tools/licences installed. You should also be able to use SQL Backup Pro to restore the files directly and leave the database ready for Differential restore. The important thing is that the backups are all done in the same chain and are therefore physically restorable, regardless of the method used to acquire them. Check it in test before you commit to it so that you know the steps needed.