I would take that he isn't going JUCO to mean that the coaches think he has a very real chance to make it... I take it you mean three to four percentile... Now jumping from 15 to 19 just on not being nervous isn't likely... but buckling down and working hard on the basics plus being less nervous and better at test taking strategies, you could probably do a 15 to 19 improvement pretty easily... but getting the next increments gets progressively harder... Still, I would guess he just needs a point or two (four to eight) to qualify and the coaches must think it realistic that he can do it.
My kids tended to hit the exact same score when they retook. They were on the higher end - so improvement is tougher, but they didn't go after it with the intensity that I would have liked... I do know of some kids who were able to jump from say a 1350 to 1450 with intense tutoring even though they were already well prepared and experienced test takers...
This makes him a Gray shirt, if he qualifies... not necessarily a bad outcome for us...