It's very hard to say whether it will or won't work or even if the system will be stable under load.
However I've seen here
that the 2GB version of the 6950 can draw ~250W when under load. ATI's requirements state 500W as a minimum to run this card.
I'd go with caution and try and pick up a 600W PSU instead just to give yourself that extra headroom.
My only concern with that case is the GPU not fitting. That being said it looks
big enough to fit a 6950.