Koa machines pretty easily - With a good router setup I wouldn't hesitate to go for it. A downcut bit will reduce the chance you get any issues, and climb cutting the sections where the grain changes direction on an outside radius (i.e. the outside edges of the bouts). Personally I like wood binding (or wood composites like rocklite) but there are a lot of good looking plastics. Just depends on the look and what you're comfortable working with.
But as the others indicated, it's definitely not necessary. If I was forced to guess, I'd guess that there are more koa ukuleles without binding out in the world than those with. You can always go ahead without binding on this uke and then plan on trying it on your next one!
If you skip the binding, make sure you get a good chamfer on the edge of the top/back plates. It'll help it feel more comfortable when you hold it, but it will also effectively give the top and back some level of protection, since the endgrain won't be exposed as fragile sharp corner susceptible to picking up every little bump and nick.