This raises an interesting question: What if Eve alone had eaten? Would Adam have been held responsible? If not, why not? If Eve had eaten and Adam chose not to, then what should he have done about Eve?
In comparison with the example given by Christ, IMHO, I believe that if Adam had simply become her covering (being the advocate and accepting responsibility and punishment for her if necessary) as his role as lord of the garden would have required, God would have considered her sin covered. Instead, Adam sins with her and when God comes calling for Adam, he abdicates his role and leaves her without a covering/intermediary/advocate. Thus God rightly punishes both.
Consider the accounts of Israel in exodus. With every occasion of gross sin and ingratitude, rebellion etc. they were always under the covering of a righteous advocate/intermediary/mediator and each time God showed mercy and grace to Israel because of the mediator.
Consider the accounts of Israel in captivity. Punished for years and exiled from their land for their transgressions, when a righteous man (like Daniel and Nehemiah) steps up and accepts responsibility for the wickedness of a people, God shows incredible grace and mercy to the transgressors and through them brings restoration.
Consider even further when there is none righteous enough to make intercession before God for the sins of the people, a mediator is appointed for temporary (yearly) relief until the 2nd Adam is come. Once He came, "He who knew no sin, became sin for us that we might be the righteousness of God in (under, through the covering or righteousness of) Christ.
Once this righteous Man is punished for our sin, grace and mercy are granted to all who are IN Him.
Reflecting back on the issue in the garden, though we don't have perfect knowledge of how God would have responded had Adam not eaten, due to the listed examples and others, I feel safe to say that I believe God would have perhaps punished Adam for Eve's sin, but it would not have been as severe, and He would have probably rewarded Adam for portraying and fulfilling the role of Adown.
I think there is a biblical principle shown throughout Scripture about the nature of God in regards to repentance and humility. If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from ALL unrighteousness. If we try to hide it,
it will be uncovered. If we repent,
it will be covered and remembered no more.