Will previous illegal employment affect application for Z visa?

I have been offered a great job with a company in China and they are ready to sponsor me for the employment license & Z. However, I previously worked as an English teacher on a tourist L, which I know is illegal.

My question is: will that affect my ability to be approved for the Z and employment license?

A few facts about my case:
1) the illegal work occurred in 2008-2009, then again in 2012-2013. The new job will start August 2014
2) I have a new passport now (with a different passport number) that does not contain any of the old Chinese tourist Ls or the entry/exit stamps, so the passport that I use to apply for the Z will not show any of that information.
3) I never registered with the Public Security Bureau in my city (Chengdu) and never had any run-ins with the police or immigration officials, and the new job is in a different city/province (Guangzhou).
4) I’m American, currently in the US.
5) I plan to explain the situation to my employer, and write a different resume that does not list my China employment for them to submit with my employment license application.

Taking all of these facts into account (especially the fact that I’ll be using a different passport and have no police record), would there be anything to alert the Chinese government of my previous employment? Thanks!