Yes - if you install a Backup, all of your Rigs and Performances will be there.
And, Yes - you should also have a Firmware update on the USB drive, in case the supplied KPA has an old OD installed on it.
It should work...
even if its an old firmware, the only impact could be on delays ( which were changed) and morphing ( can't remember when that came in but really sometime ago!).
You could ask them to tell you in advance the firmware...
There are other variables ( global settings, cab's etc) but saves lugging yours over there.
As long as you get some time with it you should be OK, I'd risk it 
Coincidentally, I installed a Backup on a different KPA a couple of weeks ago.
Doing this works even better than @V8guitar indicates - There are no miscellaneous settings to check and adjust. Installing a backup creates an exact clone of the KPA that the backup was created on. Rigs, Performances, Pedal mapping, Input and Output Settings - everything it even updates the User Name, so your Favorites can be displayed.
Amazing that the Kemper team could get some things so right and others so wrong.
Just a thought...
You might consider taking a backup of theirs before you put yours on it, so you can restore it after you are done.
This will also remove any of your own paid-for rigs from their system.
