I haven't worked with one of those, but have fixed up my share of cheapos and kids guitars.
I'd say that you should expect to replace the junk Chinese electronics. It's good you got acceptable pickups and don't need to spend on those. But do take a look at them and take note of the model number. If there are not quite good enough and have ceramic mags, you can always swap em for alnicos. Get a quality jack, decent 3-way selector switch and an Alpha A500K push/push pot to split both the hummers (if those DDs are 4-wired). I wouldn't go anything trickier with wiring than that to use than than a P/P pot for a kid that you want to focus on playing. I'd skip the bridge and/or saddle replacement, unless you end up loving this thing, then do it later. But since you are going for locking tuners, might as well swap the nut for a GraphTech Tusq XL.That will really help the tuning and the tone slightly.Then after the finish work (fret polish, fingerboard treatment, adjusting the truss rod and intonation), put in extra time to really dial in the pickup and screw height. Also, I'd start him on 10s and step down to 9s if he just can't handle 'em. 11s may solve an issue or two, but will be too much for those young fingers to use for sure.
BTW, that's a pretty cool looking guitar for a kid scale. Nice score!