While Twitter publishes no official information on the topic, user forums say that it will not send notification, because when downloading a picture you just have to right click on it and save it ("save picture as") and it'll get saved on the selected location on your computer.
If your Tweets are on "public", anyone who runs a search for a keyword in your Tweet may be able to see that message or picture. Your followers read your Tweets, so if you're hesitant to have people you may not know read your updates or check out your pictures, protect your Tweets to approve followers and keep your updates out of search. This will control who sees your updates. You can always change your mind and make them public afterwards.
With Twitter notification, you’ll only be able to see which of your Tweets have been favorited, plus the latest retweets (of your Tweets), Tweets directed to you (@replies and mentions), and your new followers.
Twitter is where news is broken, links are shared, and memes are born. It’s also a place for chatting with friends. Yet unlike Facebook, Twitter is public.
So if you do tweet with friends, it’s all out in the open by default. Check out some critical tips for new users at Wired.com.
You might also want to check these 8 twitter tips to improve your Twitter marketing, shared by Social Media Examiner.