Probably?
If one assumes, as specified in the question, that there is such a thing as God's great plan, and one grants that God is omnipotent omniscient etc. then there's basically two options for anything. Either a) it was meant to happen as it did, or b) the plan had no opinion on the matter. There is no c option of the plan being that something else happens, because if omnipotence means anything it means that things go the way you want them to.
So we're left with the possibility that God wanted Adam to sin, or God didn't care if Adam sinned. Except, the story goes, Adam sinning changed everything, threw people out of paradise, created agriculture, etc. It seems kind of odd to declare that God had a great plan and it was completely indifferent to these things happening or not.
So yes, assuming there is such a thing as the great plan and that God works as claimed and that the consequences of eating the fruit of the tree were as described, probably Adam was supposed to sin. Feel free to write your own bible fanfic challenging those assumptions, though.