This upcoming Sunday my ward's gospel doctrine class will be on lesson 23 which includes John 13-15. This afternoon I have been reviewing those chapters in preparation.
In chapter 14 Jesus promises his disciples that those who love him by keeping his commandments will be blessed by an appearance of the Father and the Son (vs. 23).
He then goes on in verse 27 to bestow peace upon those who are listening. As I read that it made me think about this statement in Jack's Welch's book "The Sermon at the Temple and the Sermon on the Mount" p.60 which says the following:
"John Durham has explored in detail the fundamental meanings of shalom [peace], especially in Numbers 6:26 and in certain of the Psalms, and concludes that it was used as a cultic term referring to a gift or endowment to or of God that 'can be received only in his Presence,' 'a blessing specially connected to theophany or the immanent Presence of God,' specifically as appearing in the Temple of Solomon and represented 'within the Israelite cult' and liturgy."
If Jesus did indeed intend his usage of "peace" in that manner then it fits the context perfectly.