No, it would not.
That's because your definition of "Person" is too narrow.
Every person has his or her own spirit.
You make the Father not a Spirit, but still, a person. You do the same with the Son. You make the Son without a Spirit, but still separate and different person from the Father. So if Jesus isn't the same as the Father, then where is the spirit that Jesus had as he walked the earth? You make the Holy Spirit a third person and the only one with a Spirit.
This is humans:
We have a spirit within our physical body.
Our spirit within us is us.
When our body dies, our spirit still lives on in consciousness. Our physical body is dead, but our spirit doesn't die, it lives on.
Jesus is from heaven and came to earth in a flesh body, but his spirit was the Spirit of God come as a man's. God the Father really came as a man.
When Jesus died on the cross, he lived on in his spirit, where he went to prison/hell, where he preached the gospel to those who had sinned and died and went even a long time ago.
Then, Jesus, in his spirit, he raised that flesh body and appeared to many for awhile, and then ascended back to heaven where his flesh body was gloried by being the first Spiritual physical body that all the saved will have one day. It is the same body Jesus had with the Father before ever coming to earth.
Jesus is the First and the Last.
Jesus had the first body of the last body we will all have one day.