We have traditionally seen most customers update firmware first, and then come back to do the drivers.
With the more recent UCSM versions, there is a maintenance policy option for user-ack, and timer automatic, called 'on next boot'.
This allows for firmware updates to be queued up pending next reboot of server,,, and then the server OS team can apply the drivers, and reboot.
Then the firmware is updated, and next time OS boots, you have have updated firmware, and drivers.
Thanks,
Kirk...