you could but i would recommend it.You have no idea if the mobo bios is registed with the gpu bios and after the update the gpu would change but the mobo bios might not start as it can't "see" your correct gpu.
i have found many reviews of this card ,and in most of them they says that they have achieved oc even far as core@950/mem@1385 so i thing the card can handle it.
my guess is either bios or the card is faulty.
my previous card was an sapphire 5770 and with the same volts (i think) it was stable with core@950 mem@1350.
but i guess you might have a point.maybe the bios is very strict on the voltage management.I guess i might use an bios editor to change that.
my sapphire vapor-x 6770 is completely unable to overclock. on the default clocks(core@860 mem@ 1200) run smooth and without a hiccup if i try to use it on the core@910 mem 1300 in 1 minute flat it will crash the whole system (or make many artifacts)
it is on a clean windows 7 x64 install...