I have doing some research on this issue since there are lots of mixed opinion on this. Per my friends who work on this matter closely, Google, Bing, Yahoo, and DuckDuckGo should all be able to fetch the React based single page applications.
Custom Mat Board (which cuts customized mat boards for any Amazon or IKEA picture frames) is a React based application, and it works well. Please check out Fetch as Google and note if there are any major difference between what Google bot sees and what humans can see. If there are significant differences, you should do something about it. But per my experience, Google bots and humans do see the same thing.
PM me if you have any questions. Cheers!
WJ
