Geometry service project operation via REST does not support datum transformation. In the case when a transformation is not provided to the geometry service project method, only 3 default transformations are used. Please see
http://help.arcgis.com/en/sdk/10.0/arcobjects_cpp/componenthelp/index.html#//000w00000205000000
For transformation between WGS1984 to NAD_1927, the default transformation used is:
esriSRGeoTransformation_NAD1927_To_WGS1984_4, forward and reverse, WKID = 1173
There are ~30 or so different transformations that can be applied for transformation between WGS1984 and NAD1927 and the results will vary depending upon which one is used. If the user is referencing the expected output based on transformation other than esriSRGeoTransformation_NAD1927_To_WGS1984_4, then the results returned by the project operation will be different.
One suggestion I have for this user is to edit/add the feature directly in 102100. Feature service will be able to store the geometry in 32023 and will use the default transformation that is set in the map.