I think the charm of ATKs is the combination of the body, the fretboard, the huge bridge, string-through possibility and the pickups. The combination of all this makes it a very solid ringing but punchy bass. Changing parts in it whole just changes the tone and style of an ATK. Some might do it, but then it's no longer an ATK and maybe it is better/cheaper/more practical to get another bass guitar.
I REALLY don't think this is the case, my Bassculture pickup hasn't changed alot of the intrinsic ATK qualities, it's just got rid of the one I had begun to dislike quite a bit. I can still hear all the ATKs unplugged acoustic qualities, they're just picked up a little differently and renewed my love for the bass.
I wouldn't call it expensive either, my Bassculture.de ATK pickup cost me about £80 - (about $170 or 130 euros), and considering the things are about £400 new, I don't see it as that much money.
Mines an old '90s Japanese one and I value it alot more then any of the new ones too, so I personally think it was more then worth it, I've never played a bass I've been so happy with the feel of, I much prefer it to a Stingray which would have cost me more then twice as much overall. Alot of other people seem to prefer a Bassculture.de loaded ATK over a Stingray too.
A pickup can only amplify what unplugged sound you already have, and while it can do this in alot of different ways, it won't remove what unplugged characteristics are there.
If your looking for something with a bit more depth, then perhaps try out an ATK loaded with a neck Jazz pickup. I love the sound of Jazzes, but I'm not a big fan of the bridge pickup, but I love the sound of bridge humbuckers, so I'm getting some routing done to get a Jazz in the neck of mine. Once I get that done and get a pre I like THEN I'll have probably spent a bit too much money, but I love the feel of my ATK and the unplugged sound more then any bass I've ever played, so I reckon it's worth it, the next steps probably to take it to a luither and spend about a grand getting a boutique copy made, but that's a looong way off.