Not necessarily.
Who were the spirits that the Lord preached to in 1 Peter 3? If the wages of sin was spiritual death there shouldn't have been anyone to preach to. They would be spiritually dead.
Right?
Right?
Spiritually dead is not a dead spirit though, its the nature of the kind of dead in respects to a person (who has a spirit)
Being "spiritually dead" can be a person who can be alive (physically so) because they have their own spirit in their body (alive in that one sense) but might be dead to God (or as one without the Spirit of God) in another.
Since the Spirit bears witness with our spirit that we are children of God and in Him we are alive from the dead (spiritually speaking) because we were not physically dead (carnally speaking) since we still have our own spirit in us (these bodies) we are able to walk around in (just dead to God) or have not the Spirit of God.
Being as one who is dead (after a carnal truth) would have neither their own spirit (or His Spirit) in them as the body (itself) without their own alone would be physically (or carnally) dead.
Jesus said let "the dead burying the dead". That was in the context of a man wanting to bury his own father before following Christ. In saying what Jesus said that even shows the ability of certain dead (spiritually so) can take it upon themselves to bury the other kind of dead (carnally so).
I just call the one "spiritually" dead (which just adresses the nature of the kind of dead one might be looking at, even in the scripture). The other one is pretty obvious, but might add the word "carnally so" to the word dead just to distinguish from the first. But again, its speaking of the nature of the kind of dead one might be talking about.
Is that person dead (carnally) needing to call a coroner (body without their own spirit) or is the person dead (spiritually) who can walk around in their own body (but has not the Spirit of Christ in them)?
Both are dead regardless (as they are both called dead) even as Jesus words were, "let the dead bury their dead".
Its simply the nature of what kind of dead he could be speaking of (as either one can pertain to any particular person at some point in time).
At least Jesus shows dead men walking (who can use shovels) to bury other dead men who cannot walk anymore .