Hi Jim,
Yes, once the BIOS has been updated you should be fine. I would recommend syncing the Back-up BIOS chip so they both have the same version, just in case there are any issues in the future and you need to use the back-up version.
To synch the BIOS chip, once you have the system up and running you will need to start up the PC and press the "ALT+F12" keys immediately, in the same way that you would enter BIOS. This make take several attempts before the key strokes are registered and, if possible, it is better to do this using a P/S2 keyboard rather than a USB one. When the process starts it is automatic and you just need to follow the on-screen instructions.
To check the BIOS versions on the two BIOS chips, go to the BIOS Home screen and then press the F9 key, this brings up a sub-menu (read only) which will give you this information along with other system details.