The AC compressor is a significant power draw on the engine. Bypassing it removes that load, freeing up engine power that would otherwise be used to compress refrigerant. This translates to slightly better fuel economy.
However, the improvement is usually modest, and the loss of climate control, especially in hot weather, far outweighs the benefit for most drivers. The amount of improvement also depends on factors like the vehicle, the size of the compressor, and how often the AC is used. You might see a slight improvement in MPG on long highway trips with the AC off, but in stop-and-go city driving, the difference might be negligible.
