You mean the whole drive. So first i would say give a try and install it maybe youre lucky and the drive work like a charm.
But i read a post from a guy with the same problem like you have and as he have installed the drive it would not work to better say the PS3 is not to work together with the drive.
What does this mean? The drive is working and eat and eject disks but the PS3 does not recognize any disk. In the past there was also a BD FW update together with a normal PS3 FW update. Now the BD´s FW is on 1.2 im guess. I dont hear any thing about that we self could flash the BD Drives. But it haves a old IDE. Maybe there is a way to flash it from PC but you will need the BD FW and i never heard or read that it would be available for us.
You should ask the Dev Team im pretty sure that they could help you to get the new BD FW but im not sure if there is a way to flash the drive.
EDIT: found some more information.
Just an update on this. We have found that "some" drives are indeed swappable but it depends on the revision of the board on the drive. If the drive revision does not match the drive doesn't seem to want to boot. We noticed a letter in a circle and then a number in the right corner of the drive board which if they match will allow us to swap the drives between the consoles. Their seems to be three major revisions of the boards.
So the question is why aren't the others swappable?
So it seems that it not depends on if the fw on the console is higher than the fw from drive. It depends on the revision of the drive board eg. diferent fws. If we cant flash the drive than the only way will be for you to get the bd fw mached to the revision of your drive board.Than you will need a infectus to dump your fw. Put in the correct bd fw and use the nand ecc tool and flash back to ps3. (sounds easyer than it will be !!! )
Or buy the correct drive matched to youre frinds original one.