Todd,
I think, it is still possible to follow the API Docs to understand the Intention behind a Code-base which Supports a Library or a Framework. In (most of the) normal cases, I would try to start with a Getting Started kind of kick-start and then gradually improve my Hello World Kick-Start by reading and applying the API understanding.
However with the constraints you have mentioned, the objective may fail if the API docs frustrates me at the beginning. If the API doc is comprehensive enough like the one I follow here, it is fine to look into those to learn and apply characteristics like,
Here comes my dramatic quote,
If Code is the Manuscript of a play or movie, API documentation should be the screen play and the demonstration that a Director would give to their actors.
In that case, it shouldn't be that hard to understand it entirely, I believe. Another great example of awesome API doc would be Node.js API doc.
Btw, the API doc example I gave first, I have been following just that to build some cool stuff on top of simple use-cases with a mobile app.
Long story short, My answer would be Depends!