The main problem is that the galactic plane is not really a plane :)
Suppose your star is located exactly in the plane, and its axis is orthogonal to the galactic plane. Then, defining "up" and "down" as the opposing directions in that star's axis, you would still have a lot of stars "up" and "down" the plane.
So, even if you only have only one disk orbiting the star, with a high enough orbital inclination, that's still visible from a lot of stars.
And of course, there would still exist a plane containing the disk's orbit, from where the disk eclipses the star.
Even more, the disk itself would still be detectable from other planes, because it's hotter than the background.
Then, if your civilization wants to keep hidden its existance, you still need to develop some kind of stealth tech for the sphere. :)
Suppose your star is located exactly in the plane, and its axis is orthogonal to the galactic plane. Then, defining "up" and "down" as the opposing directions in that star's axis, you would still have a lot of stars "up" and "down" the plane.
So, even if you only have only one disk orbiting the star, with a high enough orbital inclination, that's still visible from a lot of stars.
And of course, there would still exist a plane containing the disk's orbit, from where the disk eclipses the star.
Even more, the disk itself would still be detectable from other planes, because it's hotter than the background.
Then, if your civilization wants to keep hidden its existance, you still need to develop some kind of stealth tech for the sphere. :)