The work for a private blockchain wouldn't require graphics cards. Or much more storage than is required to store documents digitally anyway.
The video cards are only for competitive blockchain reward systems. If a bank were to utilize this system, to say backup bank-to-bank transactions, they could handle it all with a small raspberry pi setup at each location in addition to their existing database. All their documents related to the transactions could be numbered and digitally signed using the system and parsed out to various sites based on frequency of access. It would basically act like napster but with secure signage, so you know the document is legit.