While it's true that the Chinese don't have to reinvent many of the essential techniques (e.g. docking) that the US and Soviet Union had to develop in the 1960s, I somehow doubt they could make it to be moon by 2020 when they only launch one flight every year or two. From the Encyclopedia Astronautica:

Shenzhou-I: 19 Nov 1999 (unmanned, 0.88 day duration)
Shenzhou-II: 09 Jan 2001 (unmanned, 6.77 day duration)
Shenzhou-III: 25 Mar 2002 (unmanned, 6.78 day duration)
Shenzhou-IV: 29 Dec 2002 (unmanned, 6.77 day duration)
Shenzhou-V: 15 Oct 2003 (1 man crew, 0.89 day duration)
Shenzhou-VI: 12 Oct 2005 (2 man crew, 5 day duration)

To get to the moon, they'll need to increase mission duration. They'll need to increase their space lift capability substancially even if they go with an approach like EOR. They'll need to develop some form of lunar lander and presumably flight test it (e.g. Apollos 9 & 10). They'll need to develop some form of deep space network. So far, I have not seen any sort of commitment from the Chinese government to do the things necessary to go to the moon by 2020. Sadly, I don't see much of a commitment from our government, either.