It's worked about 90% of the time for me. Basically everything I've sent to kindle the last two months I've sent as EPUB, and most of it worked. A lot of them were the "Compatible EPUB" version from Standard EBooks. (Even though it says they're not for Kindle, that appears to be out-of-date.)

So I just tried Man and Superman this way -- https://standardebooks.org/ebooks/george-bernard-shaw/man-an... -- and it worked just fine. I guess I don't know if the formatting is completely correct, but I haven't had any difficulty reading books loaded this way -- pretty sure they look significantly better than the Project Gutenberg equivalents.