The butterfly effect kicks in wherever there's something unstable - whenever there's a system where little changes grow. Billiards balls do this, for instance, which is why it's harder to hit the cue so it hits the 4 so it hits the 1 so it hits the 5 than to hit the cue so it hits the 5 (assuming the same total ball travel distance).

Quantum noise is no less capable of doing this than anything else. The reason macro objects look solid has little to do with special cancellation and a lot to do with how tightly bound solid objects are. I suppose that's a special case of cancellation, but it's a really special case.

Omega-like problems are hypotheticals, and speaking of quantum indeterminacy in respect to them is fighting the hypothetical. Some versions word it so if Omega can't get a reliable answer he doesn't even play the game, or withholds the money, or kicks you in the shins or something - but those are just ways of getting people to stop fighting the hypothetical.