Well, yes and no - it is a slightly modified version, the 6510, so in that sense, yes. But in another sense, no, because what did they do, when they found thems

Well, yes and no - it is a slightly modified version, the 6510, so in that sense, yes. But in another sense, no, because what did they do, when they found themselves in need of a CPU? They used an existing design. That's pretty much what "off the shelf" means. The VIC-II would count as custom hardware, I should think, as it sounds as if it was designed specifically for the C64. Same as the Amiga stuff was designed by the Amiga team for use in their computers. And same as the ARM CPU (and the other bits) were designed by Acorn for use in theirs.