I don’t know about concupiscience but I’m pretty sure tha Jesus’ human nature experienced temptation.
**Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil. And he fasted forty days and forty nights, and afterward he was hungry. ** (Matthew 4:1-2)
Jesus recapitulates the life of Israel in Matthew’s Gospel. The Israelites were hungry in the desert. In the passage above Matthew says that Jesus is hungry too. The Israelites spent 40 years in the desert an Jesus spends 40 days in the desert. Jesus does everything that Israel had done in the Old Testament, goes everywhere Israel went, and relives the life of Israel. That’s part of the narrative thread of Matthews Gospel. He faces all the same trials and temptations as Israel but Jesus succeeds where Israel failed.
Jesus exeriences the same three temptations that Israel faced in the desert. They were both tempted but Israel failed and Jesus succeeded.
***For we have not a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin. **(Hebrews 4:15 RSV)
For we have not a high priest, who can not have compassion on our infirmities: but one tempted in all things like as we are, without sin. (Hebrew 4:15 DR)*
He was fully human. I’m sure his human nature experienced temptation. The bible says so.