They might as well invest in cold fusion, warm superconductivity, curing cancer or whatever sci-fi concept you have.
So all they have to do is wait a bit and build a frontier model of their own.
In telecomms, the late mover has the advantage of not having legacy networks to maintain, and having better technologies available at rollout time. What is the "late mover advantage" in AI? Being able to distill from every bleeding edge frontier lab? That gets you near parity at best.
So they don't spend 20 trillion dollars to achieve AGI, and in the end they still end up at parity for a tiny fraction of the cost.
How can you claim that this isn't a win?
You can't distill or catch up if you can't access the models. You'll basically have a situation where nation-states will need to try and steal the models Oceans 11 style.
In all seriousness though it is pretty interesting to consider if it really happened, a sovereign wealth fund pivots to the crazy high risk strategy, writes a blank check and tries to actually win. If it works does that country just become the rulers of the world?