When the blastocyst is a human blastocyst, yes, he or she is a person.
There is no question as to how and when life begins, that is a matter of science. The idea that some humans may be killed at will by others is a matter of philosophy or a personal belief system. A superior philosophy or belief system will serve to protect humans from killing by those who might have the power, so that human rights protection does not vary by geography or circumstances any more than inalienable human rights are dependent on anything other than the fact of being human.
Here's a great article on the subject, if you are interested in a slightly different way of explaining the facts of life:
http://unbornperson.com/section_2.htm "" THE ONLY ACCEPTABLE MOMENT FOR THE ORIGIN OF THE HUMAN LIFE-COURSE IS THE ONE PRIOR TO ANY AND ALL DEVELOPMENT, NAMELY, THE MOMENT OF CONCEPTION. It is then when the zygote was endowed with its genetic code and its human nature, which enabled it to begin its trend of development. The moment it began to develop it was already a human being, since a thing must be before it can act. Furthermore a thing must be of a certain kind in order to act in a distinctive manner, indicating that the thing must have a specific nature. And since the action is developmental, once begun, the same actor endures throughout the entire life-course of the human being, from conception until death.
THE REMAINING QUESTION CONCERNS THAT ACTOR. In later stages of his or her development he or she is called a person. It would seem reasonable that he or she be called a person at the very beginning of his or her acting. Is the zygote of human parentage a person? To answer this question one must establish the minimum requirements of personhood and to see whether the zygote of human parentage meets them.
The task is simplified by first noting that personhood is not the same as personality. Personhood, like nature, admits of no degree; whereas personality demands training, education and character development, allowing for great variety among human individuals. Personhood is the same for all. Personality is not expected of the human individual in his zygote stage, but personhood is something else and the zygote does qualify for that; FOR A PERSON IS NOTHING MORE OR LESS THAN AN INDIVIDUAL MEMBER OF THE HUMAN RACE.
The word "individual" is used in the same sense as that which indicates the relationship between one rabbit and the rabbit species. A single rabbit is an individual of the rabbit species. Two factors are involved in the concept of the individual. First, as the word indicates, the individual is an undivided whole. Secondly, the individual is dimensionally non-continuous with others of the species. Thus, the human individual is not and never can be a part of any other human individual, including his or her mother.
Reference to the individual of any species necessitates such expressions as "this rabbit" or "this man." Common usage regards expressions such as "this man" and "this person" as interchangeable. In other words, a special badge of identification applies to man. He or she is called a "person." This designation is given in recognition of man's unique and highly significant characteristic of being master of his own destiny. Every individual human, because he or she belongs to that species of beings whose members are capable of deliberate and responsible conduct, is automatically a person.
THE TEST OF PERSONHOOD IS NOT WHETHER A HUMAN INDIVIDUAL HAS EVER EXERCISED DELIBERATE CHOICE OR IS CURRENTLY IN THE ACT OF DELIBERATING, BUT WHETHER HE OR SHE BELONGS, IN VIRTUE OF HIS OR HER NATURE, TO THAT SPECIES WHOSE MEMBERS ARE CAPABLE OF SUCH EXERCISE."