As far as we know, the firmware only affects the fan operation. Are you sure it isn't the fan that has become loud? If it is truly the HDD, 2 thoughts come to mind. (1) It was there before, but you didn't notice. (2) Coincidence for the timing, and the HDD may be going bad.
The firmware is called "SMC Firmware". It is by itself and upgrades the embedded software in the computer. It cannot be combined with any other update. If you think it might make your fan louder, just skip it.