score:6
I don't know about Czech law, but in many other countries:
Just because your work is not paid doesn't mean it's not work.
In other words you may be breaking the law by doing your unpaid internship without a work permit. I strongly recommend checking with a lawyer.
To answer your question:
Yes, if your student visa is cancelled before your work permit is granted (and you do not have another permit that permits you to stay) then you have to leave Czech Republic.
Also you should be aware that a sudden switch of visa may cause you problems. Depending on how long you have been studying, if you suddenly decide that you don't want to study, but instead get a job, may lead the Czech authorities to believe you didn't really mean to study at all, but instead intended to work all the time. This may lead them to reject your work permit application.
Depending on how long you have left in your course, you might want to consider finishing your studies, doing some unpaid 'training' with your company, and starting your job when your course is finished.
Upvote:1
You are in Czech with student visa, so you must follow the rules of the visa.
If you work, the visa is cancelled, so you must return home (or in an other country where you can legitimately stay).
Probably the work permit will be cancelled and you may receive a ban on apply it for some years.
By working on student visa, you show that you do not follow the rules, so they cannot trust you for any other request (e.g. for work permit).