I think this would be a really awesome idea! Imagine it. Building halleys on the sun. Or building a dyson sphere and using magnetic containment (Science fictional universe explanation aside) Wouldn't it be just swell to suicide the sun into a planet?
With the possible exception of a neutron star, which is absurdly dense, there is no solid surface in a star to build on. And a Dyson sphere wouldn't really be impacting a sun, but a sun in a tin can, and by the time you get close, the planet will opt to impact the tin can first. Thus the only way to crash a sun into a planet is to be Archchancellor formerly-Ridcully of the Unseen University (The Science of Discworld).
If you could move the sun, that would be epic on massive proportions. xD Just thinking about playing a game and seeing the sun move away makes me laugh. Justifying putting it in-game, it would cause elliptical orbits, which would create non-stable orbits, causing possible planetary collisions throughout the map. That would be a very interesting late-late game strategy, and would give strategic importance to the sun.
Because the scale of awesomeness would break the game apart and make the machine blow up saying: TOO AWESOME TO COMPUTE
While we're at it lets fly our commanders in reverse orbit of the sun placing him in the past on chrono cam allowing the ability to save our future. Just like captain Kirk and superman