What happens if I share my post to another social network?
If someone with a private profile shares a photo or video to a social network (like Twitter, Facebook, Foursquare and so on) using Instagram, the image will be visible on that network and the permalink will be active. In other words, the photo will be publicly accessible by anyone who has access to its direct link/URL.
Keep in mind that sharing a photo or video to a social network doesn't mean that the image will be visible in Instagram. Your account will still appear private to those who aren't approved followers.