No. OldBMW is right. The engine is revving slower and therefore making less power (power = torque x revs), so you have to open the throttle to compensate. This negates any advantage of using a higher gear.
Illustration: I once towed a caravan for about 300 miles in France in an automatic V8 Range Rover. For the whole of this stretch, I accidentally left the autobox in 3 rather than D. When I came to fill up, I was expecting a massive rise in consumption. In fact, the fuel consumption was exactly the same, to one decimal place. The engine had done more revolutions, but had used the same amount of fuel, i.e. each revolution of the engine used less fuel, which indicates that the throttle was not open as wide.
(For the curious, the fuel consumption was 14.7 mpg or 19.2 litres per 100km. Ouch.)
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