Stauros:
[The Death of Jesus]
[Jesus Pierced on his Ribs]
[The Bride of Christ (Women)]
It's certainly possible that the writers who made up stories surrounding Jesus' death were alluding to the stories about 'Adam and Eve', just as many of the other stories about Jesus were deliberately written to supposedly 'fulfill' alleged 'messianic prophecies' (most of which bear no resemblance to the context of the 'prophecies').
However, that doesn't automatically imbue any special significance on aspects on the earlier story about Adam and Eve itself, which is an origin myth derived from earlier Babylonian stories (including the details about a snake and a magical plant that gives life and enlightenment), written around the 6th century BCE, which 'coincides' with exposure of Babylonian culture to the Jewish people.