Well i doubt with hallies, since there is nothing to strap them on to. Other than the core. But one would assume that the orbital laser works on everywhere else. Since a gas giant does have a core of some sort that will be blasted apart.
A planet would burn up before it reached the core of a gas giant in real life. Unless it's a more giant planet.
i don't know about throwing planets into them, but you cant use the annihilazer on them, the option to select it as a target is greyed out.
I think you should be able to knock satellites out of the sky. Someone gets all their eco from a section on a gas giant? knock those jigs down!