It is possible to get the resource path of a script attached to a node. See this question.
self.get_script().get_path().get_base_dir() # if you just want the directory
This doesn't necessarily give you the path to the scene (i.e. if the scene is inherited or if the script is shared among multiple scenes). I do not know of a way to pick a node and ask it to tell you the scene that was loaded and caused it to be added to the tree.