If add a file to books, do I need to keep the original file? Suppose I have a pdf file (i.e. some file that is not purchased through books).

If I add this file to Books, do I need to keep the original file, or does Books make a duplicate copy that it saves somewhere?

If the answer is "it saves a duplicate copy", is this contingent on cloud services being turned on?
It is not easy to extract books out of iOS' Books app once you import them. You can only take out their names, as the app treats them as purchases, not imports. So keeping a copy in Files and then opening it in Books is better.

If Mac's Books is being used, the books can be found easily by spotlight or Finder. So sync would be necessary for an easy way out. Of course there are apps which claim to go into iOS's database, but if you have a Mac, better sync. 

/Users/me/Library/Containers/com.apple.BKAgentService/Data/Documents/iBooks/Books/395687522.epub



Add PDFs to iBooks, without making a copy to com.apple.BKAgentService folder