Can the story of the shame of Noah and curse of Canaan (Gen 9:18-29) be compared to the story of the Garden and the Fall (Gen 2-3)?

This is a view taken by Sailhamer, for example. The parallels are indeed numerous. God and Noah both do planting: the Garden and a vineyard. Adam and Eve wickedly ate the forbidden fruit, while Noah drank too much of the fruit of the vine. As a result, Adam and Eve recognized their nakedness, while Noah became naked. They made themselves clothing (and God later made them better clothing); the more righteous brothers covered their father. The wrongdoers were confronted (by God, and by Noah). Finally, there followed curses, which affect the more wicked descendants of the father, as well as blessings. Clearly, the stories exhibit a similar sort of structure, and they do have some themes in common. I am not totally convinced that the similarities are intentional. Perhaps the biggest difference is that the story of the Fall—a word significant and unique, so that we capitalize it—is about the fall of man from his original sinlessness. Meanwhile, Noah’s and Ham’s sins are not quite a second fall, because they are already certainly fallen.