It really depends on the vehicle. Most of the time no, in fact many cars get worse mileage with high octane fuel because it actually contains less energy.
High octane fuels can run higher compression ratios without enriching the air fuel ratios. This means there can be a window in some cars where you get better fuel economy but it is very narrow and you would have to adjust your driving to take advantage of a very small gain.
Additionally, most cars are tuned to the fuel they recommend so most cars do not have the technology to actually take advantage of this.
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