Median Filter one after another
The answer is no:

See the following rearrangements of numbers from 1 to 81. 
In the left  case the 3x3 median of 3x3 medians will be 

median([77, 72, 67, 62, 57, 52, 47, 37]) = 57, 

in right case 
median

([5, 15, 23, 32, 41, 50, 59, 68, 77]) = 41

While the median of the whole 9x9 block is 41 for both cases.