Tea had to wait until the Tang Dynasty go gain its real importance, and it wasn't the massive trade good it became until the Song. Coffee beans, although a fairly old Ethiopian innovation, I believe had to wait until the Ottomans to diffuse. I don't know anything about kola nuts. So I do not believe so, the poor dears.

I suppose to make this a slightly less boring answer than just a "probably not", it is worthwhile to think of what we mean by the "old world", particularly as it grows more common to think of an Afro-Eurasian cultural-economic sphere. In a very real and fascinating way this is a real thing, and indeed there has been found Roman glass in Japan, and an Indian statue in Pompeii, and Baltic amber in sub-Saharan Africa. But that doesn't mean this is an integrated space and, not to wax too philosophical, the more I have studied long distance trade in non-integrated spaces the more I have seen that, by and large, long distance prestige trade does not aim for the truly novel but rather for variations upon basic themes already present with the culture. So, for example, you would find plenty of Chinese silk in Rome, but not Chinese bronze sacrificial tripods, or while you could find Roman wine in India, you would not find garum. While the exotic and the foreign have a real degree of prestige to them, there is, I suppose, a barrier of alienation beyond which they simply become weird.

Which loops me back around to the idea of a non-integrated economic sphere. If you pull the threads too far, there are probably only a few places on the Afro-Eurasian-Oceanic land cluster that cannot be linked indirectly. For example, in the year 1000 you can follow indirect exchanges from Iceland to Easter Island--although it gets very thin in some parts--but this does not mean that these areas are truly linked. Only extremely basic commodities, such as salt, iron and obsidian, can travel across many non-integrated economic spaces. While more specific items, such as Lapita pottery or olive oil, might be extensively traded within a particular integrated cultural space, they can only have limited value outside of this space, and thus will not, or only rarely, be exchanged. Or to put this in more concrete terms, during the Roman period there was a, if not exactly bustling, certainly hardily existent exchange across the Sahara between West Africa and the Mediterranean. This was the period of the Nok Culture in Nigeria, which produced an absolutely superb set of statuary remain and was very much in indirect contact with Rome. However, this trade took the form of salt, gold, and thing such as that and not a single one of these superb pieces touched the Mediterranean.

So, to loop back around again, even if these items were known within their cultural context, they would not have been traded because they did not make sense within the culture into which they would have been traded. They would have no longer been strange and exotic, but simply weird.

This might answer your question http://www.reddit.com/r/AskHistorians/comments/1hhvv3/