The product does have an auto-updater. It is hardcoded to look for updates at launch every 6 hours. It stores a timestamp, along with the current version found, in an ini file (%localappdata%\sigil-ebook\sigil\sigil.ini) in a section similar to shown below:
It may be possible to package up a pre-deployed version of this file by running the app once and then editing the last_check_time to a value well into the future. It should represent the current date and time at the time of the last check. You can run a test install to create this file (use edit->preferences to set anything else as well). Copy this file (you don't need the others) and edit the last_check_time. I would replace the portion "/0%" with "/xff%". Copy this file into the folder location as part of a post-install script. I haven't deciphered the format, but I think this sets a date way into the future.
PS: Altering the last_online_version value doesn't help once a newer version becomes available. It will be reset to the current latest version each time the app starts up.
Other customizations were not tested.
The application install has configuration files under Program Files. It is unclear as to what might trigger these being updated by the end-user.
It does not install any files to AppData local or remote by default.
It uses a file under %localappdata%/sigil-ebook/sigil for user preferences.