An ideology yes. A theocracy no.
Theocracy-the rule of a state by g_d.
Ideology- the body of ideas upon which a particular political, economical or social system are based.
A theocracy is a state ruled by religious law and governed by the clergy, so yes, Islam is a theocratic system. The fact that it is a false religion is another matter.
Islam is a complete system that allows nothing to escape it. The religious law is the civil law, the economic law, and the social law, and ultimately, the mullahs rule. Of course, ultimately, rulership belongs to the “guardians of the holy places,” the Arabs (Mohammed’s tribe), which was exactly what Mohammed set out to do in the first place.
The Shi'ites have a religious hierarchy, but they are a small minority.
The various dictators are happy to leave all of this alone as long as the mullahs/imams keep everybody happy and murder the requisite number of trouble-makers.
To a substantial degree the absence of an organized religious hierarchy serves to keep the dictators in business.