There is some recent precedent for this line of thinking. You can see here that the value of the Yen went up by more than a factor of 2 after the Plaza Accord, meaning the implied size of the Japanese economy (in nominal FX terms) more than doubled in less than 5 years. Presumably the PPP figure is more meaningful. (For related discussion, and definition of Purchasing Power Parity, see here.)
WSJ: "Sustaining long periods of strong growth is hardly unprecedented. If China edges out the U.S. in, say 2041, as a Goldman Sachs research paper predicted in 2003, it will have done so in about 65 years. The U.S. took about 100 years to surpass Britain as the world's No. 1. Japan rose to second place from the ruins of World War II in 30 years.
China has many of the advantages that the U.S. and Japan enjoyed in their ascents. Like the U.S., it has land in abundance and a sizable domestic market, which drives internal demand. Like Japan, China has a highly educated population, an undervalued currency and access to capital and technology.
China also has a history of economic supremacy, having been the world's largest economy for much of the 700 years starting around 1000. In an echo of today's capital and technology transfers, the introduction of early-ripening rice and later of New World crops like maize and sweet potatoes created food surpluses, allowing the buildup of porcelain and silk industries that dominated global trade, says Kent Deng, an economic historian at London School of Economics. As late as 1730, historians say, the country produced a third of the world's manufactured goods. China currently dominates about 12% of world manufacturing."
