He could drive his weapon to the range, drop it off, drive home and get the ammo and then drive that to the range.
I could be wrong but if the firearm was locked inside a case or had a trigger lock or cable lock installed that might be an exception.
39-17-1308. Defenses to unlawful possession or carrying of a weapon. —
39-17-1307 if the possession or carrying was:
(1) Of an unloaded rifle, shotgun or handgun not concealed on or about the person and the ammunition for the weapon was not in the immediate vicinity of the person or weapon;
I don't think a back pack would be good enough. Looks like he just needs to get a car or get a friend to meet him there with the ammo. Short anwser, I don't think he can in the scenerio you outlined.