Depends, consider all the factors...
Let's say your A/C burns around 6000lbs an hour, that is 100lbs per minute. If you can shave 10 minutes off the flight plan, you will burn 1000lbs. less for the flight time. The extra thrust will increase the fuel flow or burn rate, but it is possible to actually beat the flight plan and arrive early at the gate with more fuel in the tanks. This tend to work best for flight around 1-2 hours.
The engineers will tell you no, but line experience often says yes. There are other factors as well. Let's say a number of A/Cs are in bound at about the same time. If you bump it up and beat the crowd, again less air time = less fuel burned.
Many planes can be flown by fuel flow settings. If asked to slow by ATC to a certain speed, the fuel flow is often the same at the slower speed as it was at the higher speed, but now it will take longer to complete the flight. That means you will burn more fuel.
A quick check to see if the time vs. fuel burn will pay off is to increase the speed and then check the fuel flow to maintain that speed. Compare the extra fuel burn for 1 hour to the anticipated time savings. If you shave 10 minutes off the flight plan at an extra burn of 500 lbs. for that hour, then you saved 500 lbs. of fuel and you deserve a full can or two of soda with plenty of ice..........dammit!
There are other techniques as wells, stay at altitude as long as possible , descend at a faster IAS, stay clean longer, etc.
It is not an exact science. Every airplane has it's own bias. Some tend to burn more than others. It could be due to trim, a slightly bent plane. Just like some cars that are the same model get different MPG, so do planes. Many airlines track each airplane and figure in the bias as a percentage on the flight plan and adjust the fuel load accordingly. It's not real tangible, but it is there.
Last leg of a trip, trying to catch a commuter flight home, let it burn.