I guess not but they should, I'm currently playng on 800 stars galaxy hard difficulty, they spawned and immediatly got devastated by another empire.
Unless something has changed without my knowledge, they do not. (correct me if I'm wrong please)
It's why a lot of people complain that when they show up in a max size galaxy, they barely get noticed because their presence is essentially a non-factor when compared to the whole galaxy.
Conversely, some complain that they're too strong in the smallest galaxies, because there their presence can be overwhelming.
The Unbidden are usually fairly slow to expand, which makes them manageable even if you're not strong enough to defeat them militarily right away. Unless they spawn in or near your core systems and start immediately crippling your economy, of course.
I've never seen it happen, but later on two more factions of unbidden are supposed to spawn and fight each other.