Yes, I'd ignore adding binding if you want proper binding. If you wanted the guitar kit with it, you could probably have got a custom-ordered kit with a bound neck. But adding it now is very hard work.
You'd need to remove the frets and rout all around the edges and stick on the binding and then re-fret the neck. There are two types of binding used, single ply along the edge of the board itself and then 5-ply around the headstock. If you are able to do that, then you are probably at the skill level where you could make the whole guitar.
You'd also have to change the trapezoid inlays for rectangular ones, and add an inlay on the 1st fret.
The kits are far from an accurate copy of an SG (e.g. there is no gap between the neck pickup and the neck itself). You've also got a batwing pickguard with the kit, so to look more like that Custom, you'd need to add some pickup rings and a smaller pickguard. So, I'd concentrate on just making a nice black SG-style guitar.
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