Yes, you can add a fallback image by acting on the
Facebook will reject small images (currently images less than 200x200) but can consume and resize images up to 5 MB in size. If you have a large PNG or JPEG image you can use as an og:image you should expose it; Facebook will handle resizing for its many presentation environments ranging from a HiDPI Android home screen to a square preview image next to the story summary.
The og:image property is an array. The first valid image is used for unattended shares such as a Like Button click. If someone pastes your URL into a Facebook status message update they will be able to choose from up to three images.