Actually, no, once the 2nd stage cuts off the trajectory is mostly fixed and we know what orbit it is in. There are, I believe, two more small burns that will be done to adjust the trajectory, but these are more of an adjustment to what kind of Martian transfer orbit it is in. It already has the hyperbolic velocity to leave Earth's orbit, and enter solar orbit with an apogee at the same distance as Mars.

In 6.5 hours SpaceX will have finished everything they wanted to test with this flight I believe, including a number of post-launch checks of various systems and sensors on the payload, and those re-ignition tests of the 2nd stage.