Not likely, because the "keys" of the Gospel were given to all of the Apostles, while Mt 16 has Christ saying to Peter "I will give to you (singular) the keys of the kingdom". He further confirms this in Luke 22:32 when he says "I have prayed for you (singular) that your faith may not fail, and when you (singular) have converted, strengthen your brethren". And then there's John 21:15-19 ...
John 21:15-19 is the Lord graciously letting Peter affirm 3 times that he loves Him, after having denied Him 3 times. By "feeding" the lambs and sheep, he will be what? yes, preaching the Gospel and the Word, to them. We show our love in the same way, by fulfilling the great commission.