No. Foreign teachers would make up a small percentage of the illegal foreigners in China. The largest numbers would be from China's neighbours. Think about it, there are so few foreign teachers in China, and the vast majority have the correct papers.

It appears there is a very sizeable population of Africans living illegally as well.

From Wikipedia's article "Illegal immigration":

People's Republic of China is building a security barrier along its border with North Korea to prevent the defectors or refugees from North Korea.[63] Also, many immigrants from Mongolia have tried to make it to China. There might be as many as 100,000 Africans in Guangzhou, mostly illegal overstayers.[64] To encourage people to report foreigners living illegally in China, the police is giving a 100 yuan reward to whistleblowers whose information successfully leads to an expulsion.[65]

And from this Forbes article:

Tens of thousands of illegal aliens from Vietnam and other Southeast Asian nations are crossing into southern China each year to climb the economic ladder, as Chinese and Vietnamese officials grapple with a growing trafficking business across the porous border between the two nations.

Slightly off topic: Foreigners in China (legal) by nationality in 2011:

1.

Republic of Korea

120,750

2.

United States

71,493

3.

Japan

66,159

4.

Myanmar

39,776

5.

Vietnam

36,205

6.

Canada

19,990

7.

France

15,087

8.

India

15,051

9.

Germany

14,446

10.

Australia

13,286

Although whitey is the visible face of immigration in China, there are far more immigrants from other Asian nations. One would expect the illegal immigrant figures to reflect and magnify that trend.