[TGLS]

I think the problem here is that it is strains credibility that Austria manages establish an effective Psionic intelligence service that operates everywhere, and uses said service to keep psi secret everywhere, before anyone else even begins to start investigating psi phenomena at all. Moonshots by great powers are sometimes based on dubious propositions, but they are usually based on something. Surely any scientist who investigated psi phenomena would have published instead of keeping it quiet for the Austrians. The most plausible answer I can come up with is that somebody in the Austrian government is a powerful psi, who creates a psi training program, knowing it isn't completely dubious even though it would appear to be.

On how this would affect WW1:

1) The war is delayed, giving Austria time to prepare for the war. Maybe they manage to isolate Russia and engage in a war over the East.

2) The war isn't delayed, but Austria keeps the British out of it. France may be defeated early, and the war could end in a couple years.

3) The war isn't delayed, but Austria pulls an unimaginable number of rabbits out of their hat and the Central Powers defeat the Entente.

4) The war isn't delayed, Austria loses, but they manage to keep the minorities in line and avoid being broken apart.

5) The war isn't delayed, Austria loses, and the country disintegrates. A bunch of psychics join up with the new nations and many plot revenge against the Entente.