Hi David,
Interesting question. I'm looking at this from a little different perspective.
When you realize that John had seen the Spirit of God descending on Jesus at His baptism and heard a voice from heaven declaring Him the Son of God (Matt 3:16-17) and had so often pointed Jesus out to others, that He was the Lamb of God (John 1:29,36), and bridegroom of His church (John 3:29). I think without a doubt John knew who Jesus was.
Maybe John was anticipating his own death, so he sent his disciples to Christ so that they would have assurance that Christ was the Messiah.
I think Jesus understood why John sent his disciples to Him too.
Notice what they asked Jesus, seems to be a little bit of a question in their minds.
Luke 7:20 When the men had come to Him, they said, "John the Baptist has sent us to You, saying, "Are You the Coming One, or
do we look for another?"'
v. 21 And that very hour He cured many of infirmities, afflictions, and evil spirits; and to many blind He gave sight.
v. 22 Jesus answered and said to them, "Go and tell John the things you have seen and heard: that the blind see, the lame walk, the lepers are cleansed, the deaf hear, the dead are raised, the poor have the gospel preached to them.
v. 23 And blessed is he who is not offended because of Me."
Jesus showed them who He was by demonstrating to them and after witnessing His power I don't think there could be any doubt then. So John could rest assured that after his own death, his disciples would follow Jesus.
Hope this helped, that is the way I'm looking at this anyway
mercy, peace and love
Kat