Yes – for temporary stays, your German private liability insurance generally applies worldwide. Within Europe usually without time limit, outside Europe for one to five years depending on the policy. Holidays, workation and semesters abroad are thus typically covered.
It gets critical with a permanent relocation: many contracts end when you leave Germany for good – some immediately, some at the end of the insurance period. Premium policies offer extended worldwide validity even after moving away. Also check the coverage of rental damage to holiday accommodation and the USA/Canada clause. All details, time limits and solutions for emigrants are in the guide International Liability Insurance and under Emigrating: What Happens to Your Liability Insurance.