Is it permissible for the priest and deacon to leave the altar during the sign of peace to go and shake hands with some of the congregation?
According to the Sacramentary:
The priest, extending and joining his hands, adds:
The peace of the Lord be with you always.
The people answer:
And also with you.
Then the deacon (or the priest) may add:
Let us offer each other the sign of peace.
All make an appropriate sign of peace, according to local custom.
The priest gives the sign of peace to the deacon or minister.
Therefore, the priest and deacon do not leave the altar. To do so is an addition to the Mass not allowed for in the rubrics.
Also, the priest has just given a sign of peace (through his words "The peace of the Lord be with you always.") To do so again would be redundant.