Did Peter ever mention the church as the body of Christ?
No, Peter does not mention the body of Christ. The context emphasizes that Paul alone reveals the church as Christ's body, the complement of the head, with Christ as head in heaven and the body on earth. Peter never brings this teaching out.
Les explains that the Ecclesia is still a called-out assembly, but with one difference: this church has its head in heaven, while the body is on earth, and they cannot be separated. In Ephesians 1:22-23, Paul writes that God put all things under Christ's feet and gave Him to be head over all things to the church, which is His body, the fullness of Him that fills all in all. The word 'fullness' in Greek also means complement; we are the complement of the head. This mirrors Eve being given to Adam as his complement and becoming part of him. Paul uses the physical marriage relationship in Ephesians 5 as a picture of Christ and the church which is His body. Les points this out to show that Peter doesn't bring anything like this out at all—Peter doesn't mention the body of Christ.