Welcome to the Wefugees Community and thank you for reaching out to us.
The "Bürgeramt" may register you without a residence permit. I am not sure whether they will actually ask for it or not. However, be aware that they will report you to the immigration office (Ausländerbehörde) and there is a high chance you will get in trouble. I would highly recommend you to contact a counselling office (migration or refugee counselling, for instance). There are many organisations offering free of charge and confidential advisory services to migrants. So you won't need to worry that social workers would report you to the authorities. Please let us know if we can help you in finding a respective office in your area. In any case, also don't hesitate to get back to us with any further questions.
All the best,