Z-visa + tourist visa conlfict

Im wondering if someone can help me out. I am from south Africa. I am currently awaiting my Z-type for china as I am moving to work in China (teaching). This has taken over 3 months now and thus Im still waiting. My dilemma is- my family booked a trip to visit me in China in the anticipation that I was supposed to be over there a little while ago. If my Z does not arrive in the next couple days, Is it possible to apply for a tourist L in order to go over to china to travel/ vacation with my family? while still awaiting the Z. I understand that I might/ probably will have to come back to SA to get my Z and go back to China for work, if so be. i don’t mind doing that.

Long story short- will I be compromising my Z application if I apply for a tourist L at the same time? and is this even possible :/

Pleaseeeee help!! Thankyou :)