If there is still substantial drag torque on the nut, it wouldn't be necessary, but won't hurt anything. I will say, with nearly 50K on my bike, I'm contemplating replacing the nut at my next tire change. Self-locking nuts don't self lock forever. Without a pinch bolt, like the front, or a cotter pin and castellated nut, like the rear on my other bikes, It will be relatively cheap insurance against loosening.
Loctite never hurts, unless it's the wrong grade. 222 (blue) for most fasteners, 271 (red) for the big stuff.