My prior is that predictions are useful in general, and I have the impression this is also true for wars in general too, but I have no idea really, I just spent a few minutes thinking about it.
And I imagine it changes depending on the war dynamic. For example, predictions on mutually assure destructions would probably escalate really quickly (although not sure where it would stabilize; not necessarily high). Reason: If a prediction market predicts with slightly too high probability that a great power will do a nuclear first strike, predictors will slightly update that the other great power might also do a first strike to avoid being the recipient of a first strike, etc. in a way that can spiral and overall increase the risk of a first strike.
On the other hand, if a prediction markets signal wars would be more likely if countries had less economic trades with each other, then predicting this would be useful to inform countries to increase economic trades, and hence reducing the risk of wars.