That is what makes sense to me and seems to me to fit with the teaching of the main Christian denominations that Genesis should be seen as an allegory. The potential doctrinal bind comes later: what meaning to ascribe to the idea of the redemptive power of Christ's death on the cross, which is at the core of Christianity?
The simplistic, literalist view is that God demanded a blood sacrifice, in atonement for the Original Sin of Adam and Eve. Many people, myself included, find it absurd to conceive of a vengeful God insisting on His pound of flesh, to let humanity off the hook of being...well, just frail humanity. But for those who subscribe to this view of the Atonement, one seems to need an actual sinful act, a literal sin, to be atoned for. For which one needs a real, historical Adam and Eve.
If one take the allegorical view of Adam, Eve, however, one has then to see Original Sin differently, perhaps as I have outlined earlier, i.e. the inherent predisposition of humanity to do wrong, when it has the moral awareness not to. And then perhaps, the life and martyrdom of Christ becomes an example to us all of how we should live. This is the so-called "Moral Influence" theory of the Atonement, which is one of several, but as ancient and respectable as any of the others. More about the Atonement here:
Atonement in Christianity - Wikipedia