No, it didn't. Of course, Flatpak let me know that my user account didn't have the ability to configure the remote repositories the Foliate flatpakref specified. I could have searched for the right way to do it, but installing as root seemed to work, and it runs fine as a regular user, too!
But, of course, it doesn't. It doesn't have the ability to open files from most folders. I see by searching that you set sandbox permissions in an application manifest file, but I'm not sure I'm that attached to doing any more of this.