It does not make really sense to talk about 'binary star'. It should be a 'binary stellar system' with 2 stars involved. With this meaning, if you intend to say Jupiter is a failed star and if it had been a star we will be living in a binary stellar system (Jupiter as a star + the Sun), then yes.
Two sources of sunlight, often on opposite sides of the Earth, certainly would have changed the path of evolution, possibly even back as far as primordial slime.
