No, you can't install the connector on the server. there is no supported method of backing up the system drive, and by design there is no need to. The only things most users will have on their system drive are the users they've created (the users' personal folders are in the shares and thus protected by duplicaiton if it's turned on), add-ins that users may have installed, and information about home computers joined to the server. Also there are the "tombstones" for the files in the shares, but these will be recreated if the system drive needs to be replaced.
As for backing up the backup database, per Microsoft's design, it's essentially fungible. If something happens to it (disk failure resulting in database corruption or loss, most likely), you simply fix the external cause and recreate the database from your client PCs.
If you really feel you must back up the database, however, there is a Backup DataBase Backup (BDBB) add-in discussed over in the Developers forum. I'm fine with the replaceable nature of the backup database, but it's what I would use if I needed it.
I'm not on the WHS team, I just post a lot. :)
