Finding collisions on SHA-2 would not kill bitcoin if developers react in time. However, malicious dice would be able to cheat. Adding a nonce, as I propose, would make the system remain provably fair even in that case.
A malicious dice site wouldn't have chosen SHA-2 as their hashing algorithm if the way they're cheating is by using colliding server seeds. They'd be using a hash function with known collisions.
As soon as SHA-2 is found to have an exploit, Bitcoin mining and reputable gambling sites will no doubt start using SHA-3 (or whatever becomes the new standard).
I don't see how adding a nonce helps. If I can find two "random" strings with the same hash, I can surely also find two random strings which both begin the same nonce which also have the same hash. You're not reducing the search space by specifying that both strings must have the same prefix.