I know this is an old question, putting this here for future viewers
I can detect an error in the core engine (eg trying to call a function on a freed node) with the following code:
func _notification(what):
if what == MainLoop.NOTIFICATION_CRASH:
pass # the game crashed
Works on Godot 3.1.1
You won't get the error description, but you can tell the player that something happened in a released game