AFAIK, there aren’t any quick built-in solutions to that. What I’d do is make a duplicate of the array, apply the modifier and center the 3D cursor to that, then get rid of the duplicate, and put the other object at the 3D cursor.
Or, sometimes you can use the Multiple Snap Targets:
I.e. with an array you could just snap to the two opposite verts and find the center that way.