It is unlikely any loss of cabin pressurization caused a total failure of the fuselage. If the hull breached, the loss of pressure is a given. If the pressure was lost, one is forced to assume a small opening, because if it was a major opening, that would qualify it is a disintegration. Sounds confusing, and mostly semantics, but technically it isn't. Whatever pressure issue the ACARS message indicated, it is most unlikely to be a hull 'disintegration'; that would be expected to have engendered earlier and more critical ACARS data, meaning aerodynamic loads that were unsustainable. So it seems more likely that hull fragmentation occurred first, with an obvious loss of all pressure difference (perhaps gain?) immediately. Depending on a/c altitude at failure.