Yes, yes it does. Can everyone be hypnotized? Why yes, yes they can, if they want to.
Here's the thing, hypnosis is not a zombie like state wherein you walk around saying, "Yes, master" and do the bidding of your hypnotist ala Scooby Doo. It's not like that...unless you want it to be...
Hypnosis is more like guided meditation. You are in a relaxed state and therefore more open to your hyper intelligent internal guru called: the subconscious. No one can make you do anything you don't want to do through hypnosis, but we can help you commit to what you actually want to do.
Typically people seek out hypnosis because there is an incongruency between their actions and desires, like to quit smoking. They consciously want to quit, they really, really do; yet they keep lighting up. Why? Why? Because somewhere tucked away in their unconscious minds, they want to keep smoking. They are getting something good out of it. They aren't broken or without willpower - their unconscious brain is in control and it wants to keep on smoking.
When you are in a hypnotic state you have more direct access to the unconscious mind and can figure out how you can keep it satisfied with a new behavior. A new way of being that is right for you that creates congruency. Instead of smoking, you'll do something else, or nothing - whatever your internal guru comes up for you.
What are the good things you are getting out of being afraid of public speaking? What are the benefits of avoiding putting yourself out there and saying what you want to say?