One of the strategic lessons the East Romans learned after Justinian's campaigns to reconquer large sections of the old Empire was that large-scale occupations drain resources. By the mid-point of the Byzantine Empire (the so-called "Macedonian Renaissance"), the strategy has shifted, both in Western Europe but more importantly in the Black Sea basin (and the key strategic sectors controlling access to the Eurasian plains)--to maintaining control of only a few key outposts that could easily be resupplied by sea and from which power could be projected rapidly and quickly (e.g. outposts in the Crimea, the "Exarchate of Italy)--and which could be brought to bear to support local, pro-Byzantine powers (the Khazar Khanate, etc.).
Would Byzantine strategists have moved to occupy Iraq? Probably not. They most likely would have taken control of some key strategic facilities, and then identified locals who could take over various districts and regions.
I think that the Byzantines would have been in full agreement with the strategic vision outlined by Lawrence of Arabia that will in turn serve as the basis for an interesting essay in our summer issue by John Hulsman and Alexis Debat, "In Praise of Warlords."