They are referring to human beings being deprived of life, liberty, and the pursuit of happiness. If the unborn are human beings, they would fall under them. The only way the unborn wouldn’t fall under them is if the unborn are not persons.
No you cannot take things out of context and then ascribe them to something else. “Life, liberty and the pursuit of happiness” is not referencing abortion. Do you think that “the pursuit of happiness” is referencing gay marriage? If so then you should be supporting gay marriage.