Very interesting postulate. Indeed, Paul mentions the concept if being "dead to sin", and being "made alive in Christ". Do you have more indepth Scriptural support to offer?
I picked up that particular interpretive translation a few years ago, I believe from some studies in Hebrew on the meanings of nephesh and association with life.
I haven't stumbled back over them, but they seem to be consistent. i.e. in our scarred thinking, we too easily associate death with simply not being around anymore, whereas it is much more appropriate, IMHO, of simply asserting a state of separation.
Accordingly, once we are reborn, we are actually given a newly created spirit life, only possible by the Creator, God Himself.
This changes the perspective from perceiving postsalvation sin from a manifestation that one doesn't have eternal life, or that one really isn't yet a believer, thereby removing the enticement of works based salvation or visa versa slavation without any real volition being involved, or confusing the volition of man with the predestination of God.
Accordingly, the thrust of postsalvation life prior to the first death is to remain in fellowship with God, which only happens thrugh faith in Christ.
Passages such as "Let the dead bury the dead" also take on meaning. It also reveals a considerable depth in the mechanics or processes which transpired on the Cross. The spiritual death, the separation of soul and spirit, the separation of the body from spirit, and separation of body and soul. This also leads to which person of the Godhead was active in each step and the significance of that same person in our walk with Him.
When spaking to loved ones regarding a death in the family, the emphasis then becomes upon loving our fellow man as ourselves, recognizing the separation of a loved one from us here on Earth is indeed painful, but absent the body, the believer has essentially been promoted to be face to face with the Lord in a more glorious place.
It also nicely explains the perspective that we are saved by faith alone and faith without works is indeed dead, but not to imply without eternal life, rather dead from the flesh or body or physical domain.