True, but the emitted light is confined to two very narrow beams that rotate with the spinning star. If you aren't looking at it from the right direction, you'll probably see nothing.
Just an amateur astronomer geek here, but I disagree. As I understand it, the beams are narrow but most pulsars don't rotate uniformly. They wobble, and only a slight wobble makes the energy beams cover a fairly wide track.
And then... unless the home system had been 100% cleared out of dust and gas by the initial blast, the intense energy from the sweeping beams should still be interacting with whatever dust and gas is left in the system and lighting it up. It would have to be a very empty system not to show anything at all, from that amount of energy poured into the neighborhood. And it should still be lighting up SN remnant gas moving at slower than C when viewed from nearby star systems.
Maybe one day we'll see this in the game. It would be an interesting thing, to have to navigate a star system with a Pulsar and avoid the beam sweep.