This very question was posed on a website run by a sect called "The Christadelphians," which is one of the sects that influenced the theology of the Jehovah's Witnesses.
I think that the whole question tends to separate Christ into two persons. If He were only human, sure, He could have sinned. If He were only God, His temptations would not have been real. However, He is God AND Man. His humanity was in complete communion with God. If any of us had that perfect union with God, we would not sin. Yet, not even the saints attained to that level in this life. The entire person of Christ experienced and overcame these temptations. Just as all mankind was baptized with Him in His baptism (and our baptisms today are extensions of the one Baptism of Christ), just as when He cried on the Cross "My God, My God, why have you forsaken me," He cried this out on behalf of all humanity - so was He tempted. In Him, humanity overcomes the temptations of the evil one.
To be sure, it is a difficult question to answer. I believe too much speculation can lead us down the wrong road. I think the appropriate thing is not really to ask "Could He have sinned?" Rather, we should see that He did not sin, and overcame temptations for us, and we can do the same because we have put Him on through baptism