First let me state this...every time u want to use backup manager, you will need to jailbreak your ps3.
Now in saying this, if you have installed backup manager and start the ps3 up, it will still be there BUT will not work.. it will give an error unless you start the ps3 with a jailbreak device.
And lastly.. updating will prevent you from being able to jailbreak.
Backup manager will still be viewable but will not work.