No. The power of the keys was given to Peter, and the authority over the community to the Apostles. The Church as the holy people of God is not a Vatican II concept, it dates back to  Judges 20:2 and 2 Samuel 14:13.

To quote Lumen Gentium “Though they differ essentially and not only in degree, the common priesthood of the faithful and the ministerial or hierarchical priesthood are none the less ordered one to another; each in its own proper way shares in the one priesthood of Christ. The ministerial priest, by the sacred power that he has, forms and rules the priestly people; in the person of Christ he effects the eucharistic sacrifice and offers it to God in the name of all the people. The faithful indeed, by virtue of their royal priesthood, participate in the offering of the Eucharist. They exercise that priesthood, too, by the reception of the sacraments, prayer and thanksgiving, the witness of a holy life, abnegation and active charity.”