If its not enough power then it probably wont boot, or one cards inputs wont show anything, or something silly like that.
That being said i would definately get a bigger PSU. Even if it does run the two cards, it would be close to its max output. I would rather have a 750w+ psu running at 75% capacity, than a 600w running at 95% capacity. Your PSU will last longer that way, and leave less of a chance for a power surge to fry system parts in the future.