Does BRU perform Synthetic Backups?

No.  BRU, BRU LE, and BRU Server do not perform synthetic backups. Each BRU archive is a completely separate entity from any other archive.  With a synthetic full, the loss of any component of the synthesis process results in no backup, which of course means no restore.

How is this implemented in the BRU family of products?  Each are listed below:

BRU Server
Each machine that gets backed up, gets it's own archive.  Therefore, if you backup one machine a day for seven days, then you will get one new archive a day.  If you backup five machines a day, for seven days, then at the end of seven days you will have 35 archives.

BRU LE
Each backup that you run, will create a new archive.  However, if you choose to have BRU LE overwrite existing disk archives, those archives will be overwritten with the new job that is currently running.  It does not add to the existing archive.

BRU (Workstation & Desktop)
Each backup that is run, will create a new archive.

The above applies to both disk and tape, therefore, it doesn't matter the type of backup media, a new archive is always created.