I still lack an answer to the question, "Would God have forgiven Adam and Eve if they had repented?"
It seems to me that they did die spiritually immediately after eating the fruit. Their bodies were still alive, but they had died spiritually. Maybe God could have forgiven them at that point; but then they lied to God, or at least failed to tell the truth simply. They tried to deceive God just as Saul did when he lied and when Ananias and Sapphira lied. If the Holy Spirit is in someone, and you lie to that person, you are in effect also lying to God too.
Adam and Eve did not lie to another person; they lied directly to God. The Holy Spirit fled from them -- they had condemned themselves. They had the Spirit themselves, they knew better or should have. It is spiritual insanity to believe we can lie to God. Maybe God could forgive that sin if the person who committed it was sane enough to repent; but he's insane spiritually in a way. He's driven God away and filled himself with some deceiving spirit.
I am left believing they could have been forgiven since we are told God always is willing to forgive us when we repent; but something had happened to them that tempted them to be dishonest with God. I think it was more than "eating" the fruit that sealed their fate. That could have been forgiven. The curse of death could have been removed. It was not what went into them that defiled them but what came out. When lying words came out of them, their defilement was final.
Mark 7:15 There is nothing from without a man, that entering into him can defile him: but the things which come out of him, those are they that defile the man.
James 3:6 And the tongue is a fire, a world of iniquity: so is the tongue among our members, that it defileth the whole body, and setteth on fire the course of nature; and it is set on fire of hell.
I'm sure the Lord forgave them, but what happened to them would require a death to fix. A sacrifice for the remission of sin and death to the fallen man nature.