It is possible to create a custom tool in ArcMap that "reacts" to edits to the layer using ArcObjects. You would tie into events which get triggered. When these events are caught, your code can be run. Here is the ESRI documentation that covers events; http://resources.arcgis.com/en/help/arcobjects-net/conceptualhelp/index.html#/How_to_listen_to_workspace_edit_events/00010000031s000000/ I do not know if you can access these events using Python or the Add-In customization.
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