No, it is not. You bring it into the passage.Spiritual death is right there Jon in Genesis, as Adam and Eve lost connection to God, lost relationship, became sinners by nature, and we as in Adam are under same destiny as he was placed under, the very same curse , and being spiritually deaf and dumb to very things of God is why the Holy Spirit MUST regenerate us into being able to receive Jesus and get spiritual life again
What does God tell Adam? That on the day he eats of the fruit he will certainly die. NOT that he would die on that day. And it is simply "die, die". On the day Adam ate of the fruit death becsme certain.
How do we know this? God defined this as "returning to dust".
BUT this was a result of sin (sin begats death).
What about separation? God did cast Adam out.
BUT God cast him TO the place he was formed. Adam was not created in the Garden
Adam dying spiritually is simply not in the Bible.
You have learned a theory and then gone back to the Bible to support that theory.
But what if Scripture actually teaches "what is written"?