If 2 spaceships left Earth for the galactic centre, travelling near the speed of light, but they left an hour apart, would they arrive an hour apart?

It depends on which clock (or which reference frame) you use to measure the interval between their arrival.

If measure the interval between arrival using a clock that is not moving at relativistic speeds relative to the earth and is not in a significantly different gravitational field to the earth then you are measuring the time interval in a reference frame that is essentially the same as the earth's reference frame. In this reference frame the two spaceships take the same time to complete their journey, so they arrive one hour apart.