Not anymore, with more foreigners now leaving China it became much easier for non-native speakers to get jobs in major cities, especially if they are white.

The scenario always the same :

1. When the schools start recruiting for September in June~July they ask for white (and probably handsome only) native speakers only, because they are fool and arrogant enough to ignore excellent teachers who are not Americans, Canadians, British and so-on, persuaded that there are enough desperate people in native speaking countries who will come to China and teach for a ridiculously low salary.

2. In the end of July they start worrying because they still haven't found enough teachers for the next term and will accept non-white (and not handsome) native speakers.

3. The new term begins (September) and the school doesn't have all the teachers they need, they are now desperate and will accept anyone who can speak English and you can now negociate the contract and demand a higher salary + tons of benefits than what they offer by default.

Every year this is the exact same scheme, and every year I use this trick to get much better salaries, less teaching hours and lot of benefits, and this is for the schools located in downtown areas of first tier cities (Shanghai, Beijing, Guangzhou, Shenzhen, ...).