It wouldn't work. I don't think it would be recognized right away. I think there would be major theft and we wouldn't recognize it, and then there would be an erosion of trust and it would be a very difficult situation.
We have to start layering in provably secure communications, one-time pad or QKD for these kinds of critical things. With regard to the SWIFT infrastructure, for example, SWIFT payments and interbank lending overnight all need to be considered, because they all use a lot of third party software that may themselves have RSA leaks. It's a major undertaking, and I am aware that the banks are aware, and I am aware that our security services are aware.
However, I think that the undertaking is bigger than we've been describing. I think it's going to be a substantial undertaking because of how integrated the software world is and because there are so many layers of obsolete legacy software that are going to be difficult to go back and figure out how to patch. This is the ultimate zero-day problem, because there's no known patch that's provably secure at the moment.