Not likely. The air control valve only controls idle speed. A stuck air valve would cause either a fast idle when warm (stuck open), or the engine would idle too slow or stall when cold (stuck closed).

In any event you should still be able to start the engine. In the worst case you might have to hold the throttle open slightly in order to keep it from stalling when cold, but it should start.

Sounds more like a massive air leak, whereby the engine fires entirely off the fuel from the cold start injector. Without proper air flow to lift the air plate, the main injectors won't squirt any additional fuel.