Wise words. As has been recently reported on a popular expat forum, a new law has been passed (or, at least, will be shortly) whereby the maximum penalty for working illegaly is five years imprisonment. Whilst that may be the absolute worse-case scenario, and many strings can be pulled and palms greased before that eventuality, it is nevertheless food for thought.
However, working on a tourist/business visa whilst waiting for a KITAS does seem to be the norm at many language schools so, as long as you’re aware of the potential (albeit unlikely) consequences, it’s your call.