I don't know what the MDX specification says, but AS 2000 Books Online does document Order() as doing a stable sort - ie. the relative input order is maintained for elements with identical values:
>>
Note When the input set has two elements for which the «String Expression» or «Numeric Expression» has the same value, the input order is preserved.
For example, if the sales for USA and Europe is 300 each, and the sales for Asia is 100, the following expression returns the set {Asia, USA, Europe}, not the set {Asia, Europe, USA}:
Order({USA, Europe, Asia}, Sales, BASC)
>>