"He is a German painter."
Translation:Anh ấy là hoạ sĩ người Đức.
Not in this case. "Người" is used to indicate one person from a particular country. In the case of its absence, it usually is used to talk generally about many people from a particular country.
For example: 1. Ca sỹ người Nhật đó rất dễ thương. (That particular Japanese singer is very cute.) 2. Ca sỹ Nhật rất dễ thương (Japanese singers in general are very cute.)
Also, Đức (and Nhật) is a popular male name here in Vietnam, so it could be misunderstood as you are referring to an artist called "Đức."
I hope that wasn't too convoluted