My wife will get a Z visa to work in China as a teacher, if I get a Z visa as a dependant, can I work legally in China?

You can't legally work in China under Z visa as dependent. Now, you can apply for Z visa as dependent to enter China, and then apply for residence permit. During the stay in China, you can find a job and ask the employer to obtain the Official Invitation Letter and Alien Employment License, once you get the two documents, you can go to Hong Kong to apply for work visa, then return to Mainland China to work and apply for residence permit.