No, the story of Jesus was written in such a way to appear as though it fulfilled Old Testament prophecies. However, a number of errors make by the Gospel writers (the virgin birth, the 30 pieces of silver, etc), demonstrate that instead of Jesus fulfilling prophecy, they actually combed through the Old Testament looking for things to tie in.
For example, the whole virgin birth story is based on a mistranslation in the Greek Septuagint. It's rather strange that if Jesus existed and were actually God, that he would fulfill a recently made prophetic typo, as opposed to what the actual Hebrew scriptures said.
Consider also this: Matthew 2:23 - "And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene."
Looking in the Old Testament you find this: Judges 3:7 - "But he said unto me, Behold, thou shalt conceive, and bear a son; ..... for the child shall be a Nazarite..."
Fulfilled prophecy? No. Just another example of a New Testament writer not having any understanding of the words they were plagiarizing. A "Nazarite" is someone who doesn't cut their hair, not a resident of Nazareth. In fact, archeologists have confirmed that the city of Nazareth didn't even exist at the time that Jesus was said to have lived.
The Gospels are riddled with these types of "errors" regarding alleged prophecies. I could go on and on....