In order to hold a governorship during the late Roman Republic the magistrate needed to be a pro magistratu, specifically proquaestor, propraetor or proconsular.
Since Caesar was appointed his provinces having served a term as the senior consul, does this mean he would have held proconsular imperium for the entire 5 - later extended to 10 - year length of his governorship?
You are attempting to distinguish between the Latin term for the individual who governed a province in place of the Republic's Consuls, Proconsul, and the modern English functional term for such an individual, Governor. Such a distinction is meaningless; The terms have an identical meaning when referring to individuals who exercised consular power in a province of the Roman Republic on behalf of the Republic's Consuls.
From the Merriam Webster Online Dictionary:
1 : A governor or military commander of an ancient Roman province
2 : The right to command or to employ the force of the state
As the Governor of Gaul Caesar possessed the right to employ and exercise the power of the Roman Republic (the state) throughout the province of Gaul, and hence was by definition in possession of Proconsular Imperium.
