The Bible says, "And the LORD God commanded the man, "You are free to eat from any tree in the garden; but you must not eat from the tree of the knowledge of good and evil, for when you eat of it you will surely die." (Genesis 2:16,17 NIV)
So, before Adam and Eve ate of the tree, they apparently did not have the knowledge of good and evil. But once they ate of it, the Bible says, "The man has now become like one of us, knowing good and evil." (Genesis 3:22 NIV)
The word "knowledge" in the Hebrew is 'Yada' and it means to know, to perceive, to perceive and see, find out and discern, to discriminate, distinguish, to know by experience, to recognize, admit, acknowledge, confess, or to consider.
So, in man's original state, he did not have the knowledge of good and evil. Yet those are attributes that you would normally associate with God. So, if Adam had the Holy Spirit in him, then surely he would have the knowledge of good and evil.
Therefore, it would follow that Adam did not have the Holy Spirit in him, though he did live in a state of sinless perfection. Adam lived in a state of innocence, not knowing the difference between good and evil.
The Holy Spirit gives spiritual wisdom. So again, if he had the Holy Spirit, don't you think he would have the knowledge of good and evil?
In fact, Adam may not have even had a conscience, because a conscience is what tells us the difference between wrong and right. And he had no awareness of that, since he didn't have the knowledge of good and evil.
At the new birth, a person is given the Holy Spirit to deal with the need for victory over sin. Adam, before the fall, didn't have any sin to deal with, so therefore he didn't need the indwelling Holy Spirit.