You wouldn't be able to do missions or trade, or use certain tools or communicate with other races and all sorts of other things. If you were to have conquered every planet in the galaxy most of the game would be ruined. It would totally suck. It's unlikely that anyone has ever done this before. It would obviously take a LOOONNNNGGGGGGGG time to conquer the galaxy, and when you're done you're in for a LOOONNNGGGGGGGG period of boredom and disappointment and pointlessness. Also, some stars are too far away to reach by normal means, so you'll need a mod.