No, not necessarily. The best trade routes to Europe lay through Asia Minor at this time. As you probably know, most of Europe at this time was Christian. Christian trade could not always travel safely through Muslim lands (i.e. Syria, Egypt, Israel etc.), and whilst the Byzantines held Anatolia and Asia Minor, along with Armenia owing allegiance to the Empire, the best course for European merchants for trade with China, India etc was to via the Byzantine provinces in this area. Thus, merchants could pass relatively safely through Christian land, and the Byzantines could impose taxes, levies and duties on the goods passing through the Empire, as well as conducting it's own trade to China etc. However, once the Turks (Muslims) had control of Anatolia and Asia Minor, it was no longer safe to send Christian merchant trains through this area. Thus, not only did the Byzantine's trade with the East and the West dry up, but they could no longer exact money from the European merchants passing through their territory. And thus, nations like Venice realised they could do a better job with trade then the Byzantines, and they took most of the trade from Byzantium. With the lifeblood of the Empire (trade) rapidly dwindling, it's economy collapsed, and it couldn't hire or maintain armies, and thus collapsed.
The problem of trade with China and India and the other areas supplying exotic goods being blocked by the Muslims lasted into the renaissance, and resulted in people such as Columbus, Magellan etc searching for alternate routes to India and China.
Ah I see. And I am guessing that a quick jump by ship from Constantinople to some port in the eastern Black Sea/Cholchis area would not help at all? It's this corridor I am curious about. After all Trebizund seemed to be able to ike out a decent living in its area, I assumed it had something to do with trade along the Black Sea.