It Depends…

YES

If you place a list on the front-side of your website that is openly viewable to the general public, these files and their associated data, such as descriptions, may be indexed by search engines.

If your files need to be viewable by your visitors, but you do not want them indexed by search engines, you can prevent legitimate engines from indexing the page containing the file list by using your site’s robots.txt file. If you use an SEO plugin, look there for it.

NO

If you restrict access by setting the list visibility to USER, ADMIN or NO, these files cannot be indexed by search engines because they are behind a login.

If you are using the File Access Manager extension to Simple File List Pro, files are never searchable* unless you use Normal mode.

The upload folder itself is protected from general indexing through the use an index.html file. This prevents anyone who accesses the file list directory folder by URL directly will not see the files and folders within.

* Nginx and IIS web servers need extra measures.