I still view it as a state of being "spiritually dead". The Spirit opened their eyes to spiritual truth (as with Peter) but at the same time there was a separation that does not exist with the "new-birth".
When we look at Adam there were things that we can associate with the Spirit (God walked with Adam) and the "flesh" Adam sinned. But this is true of all men. David was a man after God's heart (which seems to indicate the activity of the Spirit) but at the same time sinned horribly . We can say this of every man (Adam, even pre-fall Adam, is no different).
The issue goes a bit beyond
@Reformed observation about applying NT terms to the OT. We are applying realities that may not have been present in the OT (Christ being a "life giving Spirit", the "age to come" which is also "now", this "rebirth").
The question about Adam's spiritual state prior to the fall is itself foreign to Scripture. It is purely philosophical (and philosophy by definition). It is fun to consider, but it would be very foolish to build upon.