Refrigeration served photographers well in the emulsion era, but I'm not sure that I'd view years in cold storage as a plus for older Vivera ink. HP specifically says that there is no need to refrigerate their ink.
The twelve Vivera inks seem remarkably stable, so you might be just fine. Unfortunately, you won't know anything for sure unless you start printing with them. I think that a significant portion of the calculated shelf life of their ink cartridges is more based on ink delivery concerns vs. ink breakdown. The seals and thin plastic membranes break down over time, and HP doesn't want to have to make good on too many failed cartridges. Out of over 500 HP 70 cartridges used, HP replaced two as defective.