This is a really neat idea... when paired with the Express middleware and Babel, you could have a pretty clean ES6 app with modern browser features and still have it work on older browsers.
A good example of this is Promises, which are supported in many modern browsers, but not all.
If you're using webpack you can use the code splitting feature to make sure the browser doesn't download that extra few KBs (which is presumable a trade-off between (an) extra roundtrip(s), so maybe you should just swallow those KBs).