Not very possible. There are typically extensive business continuity plans with multiple geolocation backups. The auditors should be making sure every financial is doing their diligence in this area. I can tell you that at the credit union I work at we test our disaster recovery plans frequently including remote working, backup office space, alternate data centers and cold storage data backups. We also structure our operations to run live from multiple locations. We might be better than most but in a real disaster most financials would be able to recover financial information with a minimal amount of data loss.

If you are talking about actual nuking then the story might be different. Not all backups can survive an EMP. I expect the biggest problem would be getting people to care about bringing the system back up. I think food and shelter would be of primary concern.