Either through the Expression Builder or Calculate in the REST Service is it possible to populate a field with a points Longitude or Latitude?
You should be able to, but you would have to have your data in a feature service for editing, because you could publish the Add XY Coordinates tool in ArcToolBox>Data Management Tools>Features> Add XY Coordinates as a geoprocessing service in order to add the coordinate fields, this tool adds the fields and calculates their values.