Flat beer diagnosis

In theory you are right, but it's such a small head space and the bottle would probably already be at least at 2 volumes of CO2 anyways.

 

Not really. Pressure is temperature dependent, but in a closed system (the bottle), any temperature driven increase/decrease in pressure occurs in both the beer and the headspace. The pressure of CO2 trying to leave the beer is offset by the pressure of the CO2 trying to leave the headspace. (In reality, it's moving back and forth, but maintaining equilibrium overall.)

So once your beer is fully carbonated to "X" volumes, it won't change.