There is some potentially useful data stored in OTF and TTF font types: the PANOSE style information (http://en.wikipedia.org/wiki/PANOSE). These flags inform host software of the most important visual characteristics of a font, so it could theoretically use another font with the same characteristics instead.
PANOSE information cannot be queried straight from InDesign, so you have to parse the raw font data yourself. Fortunately, it's rather straightforward. See this thread for Illustrator how I got it: http://forums.adobe.com/message/4171259
Unfortunately, it's potential usefulness is severly limited because it's left to the type designer to fill in the fields with appropriate values. Foundries such as Monotype and Adobe itself give it a serious try, but your average Dafont font will almost surely contain nothing but "any" or "no fit" entries.