No! It is very common to hear taught that it was possible for Jesus in his humanity to sin. They say that if it was not possible for Jesus to sin, then it was not a real temptation.
And when the devil had ended all the temptation, he departed from him for a season. [Luke 4:13]
We must be careful not to over emphasize Jesus's humanity such that we bring Him down to our level. We were born with a sin nature, He was not!
I will show that it was impossible for holy Jesus to even consider the possibility of sinning.
When defining words, we must look to God's definition instead of Webster's. Scripture uses the word tempt in two different ways.
And it came to pass after these things, that God did tempt Abraham [Gen 22:1]Is it lawful for us to give tribute unto Caesar, or no? But he perceived their craftiness, and said unto them, Why tempt ye me? [Luke 20:22-23]
One meaning is to test or prove, the other meaning is to lure away with intent to disgrace.
The scribes and Pharisees tempted Christ by diverse means, questions, and subtleties. And of this matter, says St. James, "God tempteth no man" (James 1:13): that is, by temptation proceeding immediately from him, he intends no man's destruction. [Selected Writtings of John Knox: Public Epistles, Treatises, and Expositons to the Year 1559]
God tempts to demonstrate character, the devil tempts to discredit character.
The scripture foretold that the Christ would come and be the substitute for sinners.
All we like sheep have gone astray; we have turned everyone to his own way; and the Lord hath laid on him the iniquity of us all. [Isaiah 53:6]
To say the Christ could have sinned is to say that God's plan of redemption could have been thwarted!
Events that have already taken place are unchangeable. We cannot travel back in time and undo something. Past events are forever fixed, and can not be changed. The fulfillment of scripture is even more certain.
And this voice which came from heaven we heard, when we were with him in the holy mount. We have also a more sure word of prophecy; [2 Peter 1:18]For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled. [Matthew 5:18]
and the scripture cannot be broken; [John 10:35]
God was not in heaven hoping Jesus would complete His ordained mission.
For of a truth against thy holy child Jesus, whom thou hast anointed, both Herod, and Pontius Pilate, with the Gentiles, and the people of Isreal, were gathered together, For to do whatsoever thy counsel determined before to be done. [Acts 4:27:28]
The means and outcome were both ordained by God. It was impossible for any other outcome.
And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world. [Rev 13:8]
We humans witness the unfolding of events, and call it history. God is not bound by such limitations. God does not witness history, God determines history.
Declaring the end from the beginning, and from ancient times the things that are not yet done, saying My counsel shall stand, and I will do all my pleasure: [Isaiah 46:10]
Future events in scripture are many times spoken of as having already occurred. If a prophetic event has not happened, it is just as certain to happen as prophetic events that have already happened.
God's plan of redemption will be accomplished. It is not possible for anything to the contrary to occur, or God would not be God.