Badly, but in a different way. The monastic branches of Orthodox Christianity were becoming draining, even parasitical on the Empire. People took holy orders to avoid conscription. Old, wealthy gentlemen looking to retire took holy orders to make their estates tax free (and took their wealth with them into the monasteries, aside from whatever they gave their children). The monasteries controlled too much profitable land, and the Emperor legally couldn't give them much in the way of orders or exact much from them. Had Leo not found a good pretext to take on the monasteries and break them, he would not have had the troops or funds to put down rebellion in Sicily, and possibly not hold off the Umayyads either. Constantinople is never going to be an easy city to take, but the Empire could have declined faster and harder as the Arabs took more and more from them and the Bulgarians changed sides.
Mind you, it might be interesting to see what an earlier, more powerful Arab empire could do, and how it might handle the Turks when they show up.
The iconoclast/iconodule fight was destructive in some ways; Byzantium has few good options, I suppose. But unreserved embrace of the iconodule position would have been very bad for the Empire.