Can I travel to another city during the resident permit application?

I have received the work permit already. Now applying for the resident permit, which was requested to have a 20 consecutive days of record in the Hotel (Received the certificate and given to the police).
The check out I will do only after the 20 days. But, my question is; can I travel by train back to my place (Another city in the same province in China)? Or they will trace it in the system and I may have some problems?