It does happen, but mostly by accident. Anyone experienced in eBook creation will first search the usual places to see whether anyone else has already transcribed the book they're interested in. If it has been transcribed, they will not duplicate the effort.
Etexts that are in the public domain very often float around the Net for years--stored in a gopher server here, posted to Usenet there, held on someone's local computer for a year or two and then reformatted as HTML and uploaded to a web site somewhere else. And this is good, because we want texts to be copied as widely as possible.
Public domain eBooks are fair game for anyone to copy, correct, mark up, package and post: that's what being in the public domain means.
Project Gutenberg eBooks are often quickly copied and reformatted, and posted on other sites like Blackmask at <http://www.blackmask.com> and Steve Sakoman's site at http://www.sakoman.net/.
If you find an eBook in many different places, the odds are good that it came from one original source, and was copied around.
It does sometimes happen that people duplicate the transcription of books already made into text. Sometimes it's because they didn't find the version already made. Sometimes they have a different edition, and want to transcribe that. Mostly, though, we all try not to do more work than we have to.