Yes. Definitely you can contact celebrities by following them.
That was my initial thought, too. Your chances of getting noticed are next to zero. Celebs have people trying to get at them from every angle, and I’m sure they are well immunized against all these tricks.
What good does it do you to contact someone who will never return your contact?
Totally agree!
Surely, most Celebrities have at least one Social Media Press person hosting, posting, and tweeting on their behalf?
What can you say to that person that would make them connect to you, when their job is get their message out?
I agree with you… Building relationship on social media like Twitter is the best foundation to get their attention… It takes time but totally worth it!
What celebrities posting on Twitter might affect their image on their industry, so promoting a website for the others benefits might not sounds good to them… Unless your site is really interesting and worth sharing… 
Why not? Yes, you can contact a lot of celebrities on Twitter. Because this social site is so popular in the world and everybody is using twitter to interact with their family and relatives, so try to meet your favorite celebrity.
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Go ahead there are always chances that a particular celebrity would show any interest in the subject. But that is however, rare. I have followed many celebrities and some of the famous celebrities and organizations have decently replied to my tweets.