After much noodling, looking at timelines, and making diagrams with arrows and stuff, I've convinced myself that that's not the case. Consolidation and unification was seriously underway regardless of Choi. I do think that perhaps without Choi, we'd still be calling the art Soo Bak Do, and it would not have spread around the world so quickly, but unification still would have occurred.
Like General Choi and the ITF, the use of the name Soo Bahk Do didn't come around till long after the unification movement was well established.