The two GPUs will require 500 watts themselves; to give you a complete answer (as to whether you need to upgrade your PSU) we need more info, as in, what else is in your rig. I would expect the 350 watts you have left to be able to cover the draw from the CPU, HDDs, fans, optical drive, etc, but maybe if you're running a crazy rig with like 5 HDDs in raid and tons of other power hungry stuff, its not.
Also, not all 850 watt PSUs have the connectors to run two power hungry cards like that. I don't know offhand, but I would expect a Corsair to have the right connectors.