Hi,
The act of creating/editing a feature service feature means that you are inherently capturing this information as the geometry (which includes the x,y) of each feature. If you asking whether you can customize Explorer Online to perform some action as you collect points (such as exporting to a spreadsheet or doing something else with them) then the answer is no you can't.
Given that you own the feature service my recommendation would be to use ArcMap to open the feature class itself then use the Add XY Coordinates toolbox tool (Data Managemet Tools > Features) to retrieve this information.
Mike