In terms of legal account documents - No one does physical paper as system of record anymore (it's all digitized), so survival of the documentation would rely solely on institution-specific IT policies.

If your bank hides tapes in mountains, most critical legal documents are probably going to survive. Not sure what regulations say about requirements here.

The general ledger as well as ledgers for all customer accounts are less likely to survive. Many days of transactions would be lost in the best case (e.g. PDC+DR nuked and most recent offsite is "only" 12 days old as of the attack).

How large an attack? How many nukes and what yield and where? Few of them could be deliberately high enough in the atmospheric to annihilate country wide electronics. Think one Tsar bomba in the stratosphere right in the center of America. That being said, American banks are a global animal. Some of them could have off-site in Switzerland for all you know.

EMP should take out the not MILSPEC IT and banks have excused themselves for not having backups in past behavior.