I thought I had to, but I can run the Demo at Very High (everything at Very High), without AA and without AF, at 1280x960, at 15 to 25FPS, and, surprisingly, it is NOT annoying me at all, and I think it IS playable. I'm not sure why exactly but despite the somewhat low FPS the game doesn't stutter at all, it might not be fast but it remains smooth. I don't know exactly how to describe it.
Overall I won't upgrade just for Crysis. I WILL upgrade anyway, but certainly not for that game specifically.