lol.. you only need the drive to get the patch on, you don't need it after that..
my JB has a busted drive, & it works.. perfect..
I only put in a good drive to get the patch installed, then i put the working drive back in my 3.50 ps3

once the patch is installed u can use ftp to swap patch_mp.ff & you don't really NEED to start the game.. if you download patches that have been confirmed to work, there's really nothing to it.. data transfer & you're good to go..
edit:
actually you don't even need a working drive.. you can just use ftp server straight away to 'install' the patch on your ps3.. if you can get your hands on the BLUS/BLES00XXX (whatever number it should be where you live..) & paste it on your HDD, it should work just fine