The answer is "sort of". :)

Pirates spawn like the other faction ships so they're random. They don't operate like an AI where they're actively trying to find you.

However, once they DO find you, they can send for reinforcements so it can get crazy. For instance, the other day, I was minding my own business when I saw a red blip. Turned out it was some sort of unpiloted drone "scout". It came right at my ship (I was stopped to do some mining and modifications). I don't know if the scout had targeted me originally or if it just happened to spawn on a path right at me (sometimes, they do).

So, it does the comms thing (you see a message by its name saying something like "I found something!") and I see 3 more blips as these grinder pods come at my ship. I think I ended up getting a couple of waves of those. I just ground down the cores as fast as I could so I don't know if it would've just spawned/triggered larger pirate ships.

I've had other encounters where a small pirate ship (like a fighter) found me, did the comms thing and triggered a couple of waves of larger ships to spawn and come after me.

One thing I'd say is because the mod is built on Space Engineers' engine, I think you'll have more luck with encounters (at least over time) if you scout around your local area. You'll trigger more spawns and potentially find more encounters (like pirate outposts which will call in reinforcements if you get close enough).

Also, if you increase asteroid density (assuming your server and clients can all handle it), that tends to increase the static/placed encounter density as well (i.e. you'll find more in a local area than you would with a lower density). It doesn't necessarily affect ship spawns but it can make the space around your base a bit more interesting.

Lastly, since it's Space Engineers (and assuming you're in space, not on a planet), I highly recommend converting your base into a ship (basically a flag or mother ship) or start a new one. You can jump around space and trigger more encounters and such.

If you're based around or on a planet/moon, look for Modular Encounter Spawner (MES) by Meridius. He's got a collection of mods but beyond MES (which effectively replaces the built-in ship/encounter spawner), the Surface Occupation (adds more planetside encounters) and Air Traffic (adds actual atmospheric cargo ships which SE doesn't do) really adds more to the planet gameplay.

Hope this all helps.