No, the chances are 100% because the UCI controls how teams are sent to international competitions, like the Olympics. So USAC cycling could try and exist, but their members would never go to the Olympics or other international events because the UCI would not recognize them.
UCI says “this is the licensing / governing body for this country” and everything then flows through them. They would then reinforce that decision by saying anyone who has dual membership or participates in other sanctioned races is not eligible.
This has all been done before…the IOC, and through it the UCI, governs who the national bodies are.