Language, yes. Culture? That's debatable. Athenians and Spartans went to war with each other numerous times to vie for hegemony. It took a long time for each other to identify one another as Greeks, both culturally and politically.

In my opinion, as long as technology improves towards faster communication and the lines of communication remains constant, it would allow for more cultural exchange, which then eventually leads to a world wide, grass roots cultural convergence. The best case example is the Roman Empire. Controlling most of Europe allowed for cultural exchange amongst different parts of the empire and they shared a common culture (and language depending on the areas). It was the result of the fall of the Western Roman Empire, and being cut off from the surviving Eastern part, that many regions of Europe had to adopt feudalism to fend for themselves. This led to many of these regions to form their own distinct culture, politics and language; which then eventually led to the European nation states we know today. But even so, a common European identity is starting to emerge not seen since the Roman empire. It's because of cultural exchange and improved communications allowed for gradual cultural convergence which, again, not witnessed since the Roman Empire.

If Europe is to be the model with more improved technology and communication overtime, I think a pan-national identity could be replicated worldwide. But, this will take a really long time. And I think major man-made catastrophes could happen first before cosmopolitanism becomes the prevailing norm.