I've never used React, but I believe it maintains a virtual DOM and uses it to compute the minimal number of changes that need to be enacted on the browser's DOM. So basically, it's precisely because SVG is part of the DOM that it could potentially be a good application of React.

Exactly. The React paradigm is to never mutate the DOM directly, but instead let React mutate it. I wrote a friendly intro here: http://blog.reverberate.org/2014/02/react-demystified.html