Does the GeometryService Project operation (for 10.4 ArcGIS Server REST API if applicable) guarantee that the order of the output geometries is the same as the input geometries, when passing an array of individual points for example?
Yes, the order of output geometries are same as the order of the input geometries. Although I haven't tested this on 10.4, it gives the right order in 10.6
example :-
You can change the order of the input geometries and get confirm yourself.