No. Turning up a heat pump is not like turning up a bar or fan heater. If you turn a fan heater from 1200w to 2400 watts it heats up a second bar, in effect giving you a second source of heating (and also costing you twice as much).

A heat pump has a constant level of power. It regulates the temperature by turning on and off and blowing more strongly. It does not have a ‘second source’ of heating it can switch on to increase the speed it heats up a room. By turning the temperature up to, say 25 degrees, all you are doing is telling the heat pump to not turn off until it reaches 25 degrees. THe heat pump may blow the warmed air around more vigorously to get warmth to all parts of the room, but it cannot speed up the rate at which it warms up air.