Only if you place a list on the front-side of your website which is viewable to the general public. If you choose USER, ADMIN or NO, in the List Settings these files will not be indexed by search engines.
However, if your files need to be viewable by your visitors you can prevent legitimate search engines from indexing the page containing the file list using your site’s robots.txt file. If you use an SEO plugin, look there for it.
Note – The upload folder itself is protected from general indexing by an index.html file