Yes you could, within iTunes, under the File Sharing section, as evidenced here:
https://support.apple.com/en-gb/HT201301
This functionality had seem to have gone, but I've found it now!
It's now located in Finder, once the device is in there, you click on it, go to Files, and drag the file into the subsection under the App you want the file in. It then takes a few seconds for it to show, but it's working!
So you can drag books directly into Kindle app, Adobe Reader, Word, Pages, Firefox, Chunky, etc. Any that supports the File Sharing bit. Obviously not directly into Apple Music, TV, Podcasts though, which wasn't what I was on about originally anyway.