The derailer does play a role in indexing, because it has to move the correct amount per increment of cable pulled by the shifter. This is the same for all Shimano rear derailers since the advent of indexing, except 7- and 8-speed Dura-Ace. The good part is that the odds of coming across an old Dura-Ace rear derailer are very low.

Good point about 6-speed chain possibly being too wide for a 9- or 10-speed rear derailer cage.
If this did happen, an 8-speed chain would work and shift fine on the 6-speed drivetrain though.