Yes, but they're already stored somewhere 😮 You wouldn't be able to see them at all if they weren't stored somewhere, accessible from the web. Currently they're stored in daily subfolders of https://community.giffgaff.com/assets/files/ and they could probably stay exactly where they are, yet still be indexed to the uploading member.
What's missing is that we don't (currently) have a way of displaying them together for the uploader.
One further point. Putting them in an album could actually save space for any images that are are used in more than one post. Currently they are likely to be uploaded again for each post that they appear in (and having to store them again and again for every repeat), because the forum software will not know that its an image that's been seen before. But if the photo was in an album, there would be no need to upload the photo again -- the photo would be stored once only and displayed from the album.