How well would these guys fare in 40k?

If given Auir plus the golden armada from a fortified position? And uncucked by LotV? (Meaning that some Big Bad can't just jack into the Khala without pissing them all off)

Tau equivalents maybe. I can't recall what percentage of the Galaxy they controlled, but assuming it was relatively small then they would be massively outnumbered by the Imperium and the Imperium arguably has better tech or at least comparable tech to the Terrans.

Given how their psychic powers work, wouldn't Khorne be 100% okay with even their high templar?

It's loosely like the Orks psychic powers from what I remember. But even a protoss cut off from the Khala can still use regular psychic powers.. maybe their nerve cords just serve as their communication array instead of what they use to channel powers?

They're more like a reverse Tau. Their empire used to be much larger before fracturing several times.

Not to mention how much they crave a worthy battle. I could see Khorne getting behind them easy.

The cords let them telepathically communicate with each other. Without them they need to talk like everyone else.

Come to think of it, he'd dislike the dark templar for their use of the void since it is their version of the warp, though they don't use it like how 40k psykers do.

They don't have mouths, but I believe you're right. Instead of psychic communication over long distances, they have to single each other out and send telepathic bursts. Hmm.

Well, the most basic of units would have void shields and are between the size of a space marine and custodes, so that in itself is pretty brutal. They would probably be like reverse Tau, BS2, WS4, S4 T4 with maybe 4+ or 5+ armor (since they are half naked half the time, but the void shield makes up for that) and many units being fearless. It would be a pretty awesome army to play, I think.

Given how they can talk to terrans over computer screens, they can probably instinctively vibrate the air in a way that makes audible speech.