Yes, multiple product images can be uploaded to your store via a web URL/link of an existing image on the web.
To explain, browse any website and locate an image, right click and view its properties. You will see the URL or address of this image. This is the URL you must enter to the database, which is then used to import and resize to your admin panel.
Unfortunately it's not possible to run a bulk image upload directly from your computer to the admin. Likewise, please do not place an address from an image on your computer, it must have a web address.
Product images uploaded in the gallery are not downloadable, so keep a copy handy in case you ever need it.