We could know about it in only 26,000 years due to the speed of light and gravity waves. However I’m not sure how it would affect us at all …
Perhaps there’s a burst of particles going less than the speed of light. We would know about it before those particles got here.
Perhaps you mean the disappearance of the strong gravity well at the center might affect us: I imagine any changes to the structure of the galaxy or it’s movement would take much much much longer to affect us