I would not have a living will that was activated if I am conscious. Living wills for me assume the inability for me to speak for myself. And no, I can't imagine rejecting any such request.
Just FYI if you are interested in being allowed to live even if you are disabled, you need a Will to Live, not a Living Will. A Living Will is a license to kill you outright or starve you. See the National Right to Life to obtain a Will to Live form.