That is one way to look at it. I only use the word soul because I was brought up a Catholic and that is the term they use for the infinite and eternal part of us. The thing about the soul that I find to be different from the spirit is that it is an internal phenomenon that has always been one with God and always will be. The connotation one can take from spirit is that it is somehow separate and apart from God, thus giving us the idea that the spirit returns to where it came (and also the idea that there was a time when the Holy Spirit was not with us as many believe it did not come until after Jesus breathed on the apostles). The truth I found is that God is always everywhere so how can the spirit return to God if it never left? The distinction I am making is that the soul is one with God. I find this to be the bottom line of the scriptures but somehow there always seems to be something more important. I think we can substitute spirit for soul and almost use these words interchangeably but please mark my point: we are one with God because of the soul.
The only ones that are one with God and posses his Holy Spirit are those who have come to Christ to be saved by him.
Paul said to the Galatians... "Did you receive the Spirit by the works of the law (because you did something) or by the hearing of faith?" (hearing and believing the Gospel)
The Holy Spirit is only given to those who hear and believe the Gospel. If you are not trusting in the saving work of Christ you are void of the spirit.