No, if you travel away from Earth at a faster velocity, it does not cause Earth to orbit faster around the Sun. The orbital motion of a planet like Earth is determined by its mass, the mass of the Sun, and the distance between them, rather than the velocity of an individual object within the system.
According to Kepler's laws of planetary motion, the orbital period of a planet (the time it takes to complete one orbit around the Sun) is primarily determined by the semi-major axis of its elliptical orbit. The semi-major axis is essentially the average distance between the planet and the Sun.
In the case of Earth, its average distance from the Sun is about 93 million miles (150 million kilometers). This distance determines the length of Earth's year, which is approximately 365.25 days.
Individual objects moving away from Earth or traveling at different velocities within the Earth-Sun system do not significantly affect Earth's orbital period. Earth's orbit is a result of the gravitational interaction between Earth and the Sun, and the collective mass of all the objects within the system.
So, traveling away from Earth at a faster velocity would not cause Earth to orbit the Sun faster. Earth's orbital period remains constant regardless of the speed or direction of individual objects within the system.