Possibly, but I'm not sure about those - wasn't Anatolia and Italy more affected than the parts that fell to the Arab empire?
I also think it was the stupid in-fighting caused after Chalcedon AND the persecution of the Jews
when the Arabs took over the Levant, Egypt and North Africa, the Copts, Syriac Christians as well as the Jews helped the Arabs take over - the Arabs were initially "our religion is ours alone, we don't want none of you losers"
The Volcanic Winter was world-wide, significantly effect crop production - famine. Justinian’s Plague was particularly hard in the east. Both effected populations, hence effected trade, economies and the ability of the Eastern Empire & Persians to maintain and raise troops. As you pointed out both empires had devastated themselves with a 40 year war, the pressures of the plague and Volcanic Winter left a scarcity of resources to rebuild. They became a hollow shell. The Arabs essentially punched an empty bag!