Not exactly only through him our we without sin,like when we do something in the spirit,we in general still have sin,but yes he paid our penalty of sin"old sin" so that we would be no longer a "slave to sin" our ultimate freedom from sin is after judgement day for we will not be in the flesh having new bodies.
Imputation
Imputation is used to designate any action or word or thing as reckoned to a person. Thus in doctrinal language
(1) the sin of Adam is imputed to all his descendants, i.e., it is reckoned as theirs, and they are dealt with therefore as guilty;
(2) the righteousness of Christ is imputed to them that believe in him, or so attributed to them as to be considered their own; and
(3) our sins are imputed to Christ, i.e., he assumed our "law-place," undertook to answer the demands of justice for our sins.
In all these cases the nature of imputation is the same ( Romans 5:12-19 ; Compare Philemon 1:18 Philemon 1:19 ).