Yes, the photos & videos shared through iCloud Photo sharing can be saved or downloaded by anyone who can view the shared album. However, videos can only be downloaded to a Mac machine or a PC. You or anyone else can not download shared videos on an iOS device from iCloud.
- On the compatible iOS devices, you can save & download photos to your 'Photos' tab or 'Camera Roll'.
- You can add or copy shared photos & videos to your library in iPhoto or Aperture for Mac.
- On a Windows PC, you can copy shared album's photos and videos to any folder.
- On the web, you can download photos and videos directly to your computer from the detailed view of each photo or video.