Those AIs would be in a similar boat to Tau, who practically don't have souls. Too young. That's why the Tau are mostly immune to chaos corruption, and possibly why they have to use shitty realspace travel instead of the warp. Though the Ethereals might have some kind of psychic power, they're weird. Might not be warp related.
It is just pure inspiration, comrade
Do you not believe in the True Message of the Ethereals? That is okay. We all doubt sometimes. The Enthusiasm Assistance Centers are just down the street, just say Aun'nel Trustbound sent you. They'll fix you right up.
(Wait, "Aun'nel" would be... talking to a gue'vesa?? So egalitarian!)
"Oh thank you, I'll report right away! I didn't realize I was faltering, but if you say so!"
What's silly is that I was thinking of stuff like the holo clones ethereals can summon in Dawn of War, which are almost certainly just advanced technology not psychic power. I wasn't even actually questioning the love for Ethereals. They're just great!
I guess for "win conditions", Tau would need a better FTL drive. That would let them find even better minor race allies, and probably kick off that afore-mentioned geometric expansion. Especially since Tau can sometimes annex human worlds through diplomacy (backed by military power). They really just need raw numbers to utilize their tech advantages, imagine if they managed to win a full hive world. Gue'vesa in Imperial Guard numbers but with pulse rifles, mmm... Imperium would have to devote a lot of resources they can't afford.
If they did overrun the galaxy they'd have countless safely-regulated psychers, the STCs, and extremely advanced understanding of biomorphic organisms from their Kroot. So I could see them taking on the Tyrannid mother fleet.
(maybe even find a way to purge defeated Ork spores with nanites... nah, Orks are eternal.)