InDesign also has its own predefined symbols for displaying invisible characters when Show Hidden Characters is activated, independent of what might be encoded in the font.
FWIW, TextWrangler does appear to actually display the encoded outline for discretionary hyphen U+00AD. So, in Nick’s example above, pasting such a text into TextWrangler makes the discretionary hyphen point visible. As far as I can tell, if one is not encoded, it will use a fallback font. (Not a good reason to draw one, I’m just reporting . . . )
But this is a text-processing and coding app, not a layout app. Most people don’t go around applying different fonts in TextWrangler. ;-)