Any question answered...

but surely the easiest way would be to print the parts separately (plates, pins, bushes) and then assemble

There isn't much point printing them if you then thrown them into a chain assembly machine anyway, not to mention that 3d printing isn't up to the dimensional tolerances and material properties required yet. Even if you're only making 1 chain, you need 112 pins, 112 rollers, 112 bushes, 112 inner plates and 112 outer plates, so it's not a prototyping process, it's a small batch production. You might be able to make the punches and dies to cut your plates on a 3d printer.