If you can do it with PHP, you can do it with WP, but it could involve custom coding. So I’d answer with a qualified yes. The best approach depends on how and where you do the uploading. If you are using the WP media upload facility, you basically have a list of uploads in the media library which can be sorted by date and other criteria. If you need a differently formatted list or one available on the front end you could build a custom page template to generate the desired list.
Even if you do not upload as media or if they are not in /uploads/, for example, files uploaded via FTP, you can still build a page template to get the files in a particular location and generate a listing of files there that are newer than a particular date.