The plugin creates an popup window which is basically a minimalistic version of your website, which does have the login options available and it does remember if the user is logged in or not.
In fact I would like my forum members to be able to use the upload module without creating an account. I would have liked a pre-configured (by me) account in the module.
Make those images available only from your forum. If the thing will be used only for your forum then simply make the images allowed to be seen only if the request comes from your forum.
To do that you need to add a rewrite condition in your .htaccess (Apache) or server block (nginx).