I was under the impression that you can, though they might show up under Documents rather than Books - assuming you've side-loaded by sending the files to your kindle e-mail address. It's not something I try to do very often though, so I might be mistaken - they don't seem to appear in the Cloud Reader though.

In any case, since you can just open the files in the desktop version of Kindle, it doesn't seem like it would be such a big deal.

It's annoying because I rely on Kindle's progress syncing. Why do some of my books randomly not support this useful feature?