It's probably the other way around: stability held increase the viability of the Silk Road. The Silk Road ran through a few large, stable empires including Han China, Parthia, and Rome (along with various Indian kingdoms and empires, including the Maurya Empire for a little bit). The ability of these large empires to control their territory and maintain peace (e.g. Pax Romana) allowed trade to become more pervasive.

An interesting parallel can be drawn with the rise of trade between Europe and Asia during the 13th century. While there were many causes for this (including the rise of trade empires like Venice and Genoa, renewed relations between Christian and Muslim lands, etc), the stability brought by the emergence of the Mongol Empire helped allow trade and travel to become more common between East and West. Early accounts, like those of William of Rubruck, and later accounts, like those of Marco Polo and John Mandeville, illustrate the general typicality of the contact between East and West.

The emergence of the plague, dissolution of the Mongol Empire, and rise of more powerful and expansionary states in the Middle East (namely the Ottoman Empire) helped cut off Europe from the East, until the Age of Exploration.