>>13215971No it does not. This is because even though the front and rear occupy the same space they don't do that simultaneously. The rear is always in the past and the front is always int the future.
If you imagine a closed universe as a circle where time is moving in the z-direction the space ship is going to wind up in a helix in spacetime and never collide with itself because its parts always exist in different time.
This question is addressed by this video
https://youtube.com/watch?v=6MfJ59lkABY