The answer to this is yes, sort of, with caveats. I talked a little bit about this "imported terminology" in relation to China here, and how even though terms like "ancient" "classical" and "medieval" do not fully translate to a Chinese context they still convey useful ideas and are a way to escape the strictures of dynastic periodization. For example, the book Medieval Chinese Warfare makes a very strong case that the period between the fall of the Han and the rise of the Song is in many ways better thought of as a single period--the "Chinese Middle Ages"--rather than the complex sequence of dynasties and interregnums that it is traditionally portrayed as.

Beyond that, in recent years there is a growing scholarship around the idea of a "Global Middle Ages", a period in which the spindle threads of interconnectivity across the Afro-Eurasian land mass developed into something more sturdy and substantial. The introduction to the Oxford Global Middle Ages project is a good place to start if you want to read something substantial about the historiography of the concept, but broadly speaking it developed due to a dissatisfaction with the traditional idea that placed the "birth of globalization" in the "Early Modern" period (for simplicity's sake, let's pin that in 1492). It also owes a great deal to the increasing scholarship on Islamic sources, in many respects the "global Middle Ages" can be seen as a product of the spread of Islam as the linkage between a variety of disparate regions, particularly in the heart of Eurasia, and Muslims as merchants, scholars, pilgrims and warriors. The archetypal figure of this is the traveler Ibn Battuta, who in the fourteenth century travelled from Morocco to Sumatra and back finding hospitality and work in his role as an Islamic judge. This unity at the center powered an intensification of the commercial and cultural connections, ideas and goods, and it is impossible to understand why someone in Spain would want to sail around the world without them.

Speaking as someone who has studied the ancient world with a focus on long distance commerce, I do have a few contrary thoughts on this, in particular the degree to which this represented actual intensifications of global contact vs the spread of a cultural milieu (Islam) in which writing was common, in other words is this an illusion of our source base? How do we deal with the question of the enormous volume of trade between the Roman empire and India, the spread of Buddhism across eastern Eurasia, and the great pre-Islamic centers of central Asia that are tragically near lost to history? Not to deny the concept of the "global Middle Ages" merely to put a pin in the thought that it is somewhat open to the same critique as it had of "early modern globalization".

Probably the most best popularly available source on this is Valerie Hanson's The Year 1000: When Explorers Connected the World.