Both the systems used in the reviews below were Nehalems, so more power hungry than the i5 you have. http://www.anandtech.com/show/4061/amds-radeon-hd-6970-... http://www.legitreviews.com/article/1488/18/
They show maximum power consumption between 479-509W. The Legit numbers were taken from the wall, this is likely true for the Anandtech review as well, but I haven't seen it explicitly stated anywhere.
If they are taken from the wall then 10-20% can be taken off to get their actual system power draw and I think that is good number to use as a worst case for you.
A 460W load would only stress a 620W PSU to 75%. So it is within the capabilities of a 620W PSU to power a build with two 6950s. However no 620W unit I know has four PCIe connectors, so you would have to use adapters.