Bizarre, I was under the impression that only Muhammad's face is not allowed to be depicted and all... I guess I'll have to do more research on Islam, but still, I do not know whether printing the face of Jesus on coins would be a sufficient motive for the Arabs (or the Byzantines for that matter) to stop trading with each other. Remember that trade is not done by the Caliph's or the Emperor's courtiers, but by merchants, who are most likely driven by profit first, and beliefs second. Of course as long as the profit does apply.
Concerning both economies being hurt, I think it is a logical conclusion of what happens when two powers stop trading with each other. Now, depending on the relationship, one will be hurt more than the other; one of the two might even be hurt in such a miniscule way, that there will be no overall difference. I guess that, in the end, to see whether either side benefits from not trading with the other at all, we must find an estimate of the volume of trade between the two powers in this historical era.
Trade did indeed continue. As for the merchants on both sides, many were prepared to turn a blind eye, but as with a lot of things that exist at an official level, it did affect things higher up the chain. It did have detrimental effects to both sides, but for Justinian, the benefits outweighed the negative bits, and he was well satisfied with the problems and hand wringing it caused in Damascus whilst it lasted.
Exports for the empire were not affected too much since it was the Arabs who were paying with old Roman coinage and their own. That didn't bother the Romans too much. Imports on the other hand were more affected since as the Romans used more of the new coinage, it rubbed up some in the Caliphate the wrong way. Actually you'd get the bizarre phenomenon of Roman traders preferring to use older coins and Arab ones too. Better for business after all. Still, profit wins out in the end, and once the furore had died down, as it always does, merchants of course just get on with it. But certainly, when it was first introduced, it didn't help diplomatic relations much for a while.
Interestingly, Caliphate coins, since they were closely modelled on Byzantine coins were used a lot in trade too, and you'd find them quite easily throughout the Roman Empire.
Sargon