Sorry this isn’t a full answer, but yes this probably is possible but you need to run a database query or some code to find the images, and then do something with that list such as copy the files to a new directory.
There’s info here on how featured images are stored.
Here’s a quick suggestion based on that post, written as pseudocode, but if it’s what you want and you know how to write a bit of WordPress PHP this should be quite easy and potentially save a ton of time if you were going to do this manually.
foreach ($allPostIDs as $postId) { // get all post ID's somehow and loop through them
if(has_post_thumbnail($postId)) { // if post has featured image
$fileInfo = get_attached_file(get_post_thumbnail_id($some_post_id));
// do something with the file info, like copy all files to a new directory or output to screen
}