ECDLP rather than SHA256 as Adam_xx has pointed out, but regardless, I don't think they would be stolen in quick succession.

It will not be the case that ECDLP goes from "unsolvable" to "trivial to break" in a single step. If ECDLP does become broken, then the first time someone breaks it it will be because they ran a quantum computer for days or even weeks to break it, meaning they can at most empty a single address. Then they will have to start again for another address, and another, and another, and there are tens of thousands of vulnerable addresses to be attacked.

Quantum computers will get faster and more efficient as time goes on, so eventually it may well be possible to crack an address in a few seconds or minutes, but that certainly won't be the case to begin with.