No christ did not have a sinful nature(adamic nature)but he could have sinned........please allow me to explain.
Jesus was all man yet all of Deity dwelt (tabernacled,housed)within that house of flesh...................He was not subject to a sinful nature as you and i because of the fall of adam due to the fact he was not concieved as you and i...........He was born of a virigin(a women who had never known a man)...............Yet he had the ability to sin because of one little aspect(FREE-WILL).........the bible says he was tempted in all points as we.......yet he chose not to seeing the glory that lay before.
We see just how human he was by the out cry LET THIS CUP PASS......but yet we see FREE-WILL come into the picture by the following statement NOT MY WILL BUT THINE BE DONE................