No. The indexing is speed specific (at the shifter).
An 8sp shifter pulls a set amount of cable to move a shift. A 9sp will move a different amount of cable.
However, the derailleur isn't indexed. All the way up to 9sp, the distance a derailleur moves per unit of cable movement is identical. At 10sp, Shimano changed the distance the derailleur moves per unit of cable Movement, so you cannot use a 10sp MTB derailleur with a 9sp indexed shifter (nor the other way round)
That's interesting, I didn't know 10 speed derailleurs moved a different distance for a given amount of cable pull. Is that true for sram as well as shimano? If I ever venture past 8 speed I'll have to remember that, I am an inveterate mix & matcher!