IMO this seems to get "precariously" close to the Catholic doctrine that rightpoeunss is not strictly imputed at justification, but given/infused. And, why in fact, would new creations in Christ bother to act righteously unless they were now, in some manner actually given righteousness, even as the essence of that righteousness is the very union with God that Calvin speaks of?
This is hard, because righteousness has a range of meaning, from an acceptable status before God to being moral.
I think in Calvin (and Paul) righteousness is both imputed and infused, though they don't use the term infused. But these two things are conceptually distinct, although not separated. Justification is imputed righteousness. When Paul talks about justification by faith, I think he's using righteousness primarily to mean proper status before God. God recognizes faith as a sign that we are his, and calls us righteous. (Calvin apparently doesn't understand that righteousness can refer to status, and thus thinks that God is crediting us with Christ's moral righteousness. However in the overall scheme this is still imputed righteousness, as opposed to the infused that I'm about to talk about.) N T Wright suggests that we are recognized as righteous based on faith in part because of the changed life that God knows will result.
But in Rom 6:16 Paul uses righteousness as the opposite to sin. That gives it a moral character. Rom 6 suggests a kind of righteousness that results from our union with Christ, dying and rising with him. Paul doesn't call it infused, but it's not an impossible term. Calvin comments on this in the following terms:
"Moreover, lest by his cavils he deceive the unwary, I acknowledge that we are devoid of this incomparable gift until Christ become ours. Therefore, to that union of the head and members, the residence of Christ in our hearts, in fine, the mystical union, we assign the highest rank, Christ when he becomes ours making us partners with him in the gifts with which he was endued. Hence we do not view him as at a distance and without us, but as we have put him on, and been ingrafted into his body, he deigns to make us one with himself, and, therefore, we glory in having a fellowship of righteousness with him." (Institutes, 3.11.10)
But Calvin is clear that this is a result of being in Christ, and not a prerequisite for righteousness to be imputed.
The Reformed tradition is known for coupling works more closely with justification than some other Protestant traditions. Thus there are Protestants that think we do in fact come too close to the Catholic position. The situation is further complicated because the Catholic and Protestant traditions use different definitions of justification.