Negative.
If the barrel is parallel to the ground, the bullet will never be higher then the barrel. What you think is the parabolic effect of the bullet is actually caused by the sights, especially evident in the M16. To line the sights of an m16 parallel to the ground, the barrel of the gun has to be slightly pointing up, this is why the bullet strikes the same spot on the paper at 25 meters and 200 meters (I may have the ranges incorrect, but you can zero an M16 at 300 meters, or at a much lesser range with the same outcome). The sight is parallel to ground, the rifle fires UP to the 25 meter target, apexes at about 100 - 150 meters, and impacts the same area of the target at 300 meters as the bullet is on the way down.
If there is ANY lift to the bullet due to it's rotation, it's negated by the downforce the rotation submits to the opposite side of the bullet. (reason a planes wing is not the same shape top and bottom).
now if the rotation was front to back, or back to front, and not side to side, MAYBE the bullet would rise due to heat and friction.