Tony, perhaps you are suggesting that Adam should have been more incredulous towards his creator? Note that Adam watches the woman to see what happens when she eats, so it's not clear that he truly believed, but may have been afraid to act.
Second, Adam didn't know good and bad (see Genesis 3:22 that he "came to know good and bad" - that is, he did not know it before hand). So it is unclear to me how Adam and the woman (she is not named Eve until later - and name changes MATTER) would know right from wrong. How would they know it was good or bad to follow the command of God?
To me, this story seems like the inevitability of our condition, not some moral story. I would say to directly provide my answer to your question: You ask "should" Adam do x. I answer, "should implies something good/better than what is." Adam had absolutely no basis for making such a determination, and we are looking back at the story through the delusion of the knowledge of good and bad which Christ was free from (See Matthew's model of Jesus in Isaiah 7:14-15).
Isaiah 7:14-15, Therefore the Lord himself will give you a sign. Look, the virgin is with child and shall bear a son, and shall name him Immanuel. 15 He shall eat curds and honey [in paradise/Eden] before he knows how to refuse the evil and choose the good.
Deuteronomy 1:39, "your children, who today do not know right from wrong, they shall enter there;"
And Christ repeatedly says that we must be children to enter paradise.
The answer to your question is "no." But not because your question has a yes or no answer, but because your question is broken in an important and fundamental way diagnosed by Christ.
The Japanese have a third answer, "mu" which means "un-ask."