No. Not all statues were intended to have arms. We are familiar with a bust. It is a statue of just a person's head. Some statues have no arms. To make them look less like amputees they make the arms look like they were just detatched.

Between galaxies which are gravitationally-bound it should not. When moving through intergalactic clusters which are not gravitationally-bound, yes. The problem is, compared to the speed of light (the cosmic speed-limit) the expansion of the universe in these areas prevents any relative motion when traversing toward an object on the other side which is being thrown in the opposite direction. When moving laterally between galaxies which are weakly gravitationally-bound the effect will be minimal given light-speed is so slow to cross the distance over millions of years, most other forces will have a greater influence