I Am Not An Economist, but, the problem with infrastructure is that its difficult to know where to put it to generate a reasonable return on investment- predicting whether a new road gets used or a new residential area becomes desirable is more of an art than a science, and if you get it wrong you've essentially thrown money out the window. China has had this issue in spades- witness its infamous "ghost cities"[1]. In the long run, China's infrastructure growth (and therefore, to at least some degree, growth in general) will be limited not by what people are willing to spend on it, but peoples' understanding of the exact shape of what they're building with it.
[1] http://priceonomics.com/surveying-the-ghost-cities-of-china/
So there will be bubbles, but I have little doubt that they will have a higher growth rate than the west for quite a long time. Once they become fully industrialized, probably not.
We can tell the same story about India, BTW. The last deca might have been terrible for the EU and the US, but it has been amazing for Asia. It's only not been quite as good for Africa because so many countries the hare horrible governments.