The question needs to be divided in order to distinguish what is proper to the person and what is proper to the nature.
"Man," with reference to his human nature is under law. Righteousness is a law-term. Therefore the righteousness imputed is that which is demanded of men by the law. Being imputed that "person" is accounted righteous, but the righteousness is suited to the human nature of the person. Our Lord has two natures, not one. In working righteousness it is the work of the whole person. His divine personhood gives it infinite value, but the nature of the righteousness which He wrought is bound upon the human nature of our Lord. Hence "made of a woman, made under the law."
Concerning the negative part of the question, yes, it is not the divine attribute of righteousness which is imputed to the believer. As applied to the believer righteousness is a law-relation, whereas God is absolutely and originally righteous in Himself.