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According to this page, the sup does support the X2-10GB-CX4: http://www.cisco.com/en/US/docs/interfaces_modules/transceiver_modules/compatibility/matrix/OL_6974.html#wp48759
It looks to me like it has not loaded any IOS. Connect to the console port of the 2nd Supervisor in slot 6 and make sure it is not stuck in ROMMON mode. If it is, then boot the same IOS as the active supervisor.
Yes, the config will still be there as long as you save the running configuration with the write command (simply type "wr"). For peace of mind you can save a backup of the running config and vlan.dat to the supervisor's internal flash memory or an ex...
I'd say your best bet is to use TFTP to transfer your config and vlan.dat to a server and then power down the device, swap the sup's and the line cards over. The line cards are hot swappable but as you're replacing the sup the system will reload anyw...
