I believe that Christ being the 'Son' of God would certainly have allow Him the power to sin. If not, then what was the purpose of 'His' death upon the cross? Doesn't seem like over-coming sin would be a very great achievement if sin had no power to corrupt that which over-came it. Any other answer would certainly negate the instances that we have of Christ praying for strength to do what needed to be done. If there were no chance of failure, He wouldn't have needed to pray for strength.
God is unable to sin for there is 'no other' that holds authority over Him. Our sins are against our brothers and against God. God can sin against no one or anything.
Christ on the other hand was flesh and Spirit. Satan would never have tempted Him if it were 'impossible' for Him to sin. Christ was our example and we are to follow in His footsteps. If somehow He were completely immune from the ability to sin then we certainly have a God that has been unfair to us.
We too are told that we, that accept Christ and follow the will of the Father, are the 'Sons or God' also. Regardless of how people deny this literal fact, that's what we have been offered and only have to accept it to bring it into our reality.
We continually try to change ourselves instead of allowing God to do it. For this reason, we continually stray away from the Father. You cannot NOT sin by trying. The elimination of sin is accomplished through the change of one's spirit. The only way this can be done is through the Spirit of Christ and God's will.
Stop struggling and submit. You will not change over-night. This is one of satan's most successful lies. Many believe that upon acceptance their lives will become 'perfect' over-night. NO, it is a gradual thing at first that will grow continuously through ones walk. Give those sins to God and let Him take control. Once you admit how weak you really are, your pride is abandoned and God WILL take over.
That's the biggest difference between Christ and us. He abandoned his 'self' to the will of God. We were told that we too could produce miracles through the Spirit if we could just let go of the world and self. Faith my friends is not just a belief that Christ or God exist, it's the belief that they are in control no matter what and that your best interests are their goal. Acceptance of this fact is the faith the we must have.
This is what aided Christ in His walk through this world. He didn't sin because He allowed the Father to lead Him in EVERY STEP. He abandoned His 'self' for the sake of all the people of the world and allowed God to be his guide. There is much power in the knowledge that God is there for you no matter what and Christ KNEW THIS.
He certainly could have sinned, but through His love for us and His Father, he over-came it, and defeated death for those that believe.