Not exactly; there is one power supply that provides the energy to the five (or however many) power amplifiers that are in the receiver. The only amplifiers that can be active are the ones connected to speakers.
5.1 surround actually has six discrete audio channels (five full range channels and one bandwidth limited channel), those channels are fed into the processor, the processor then sends each incoming audio channel to the correct amplifier (or preamp output) in the receiver.
There is a finite amount of voltage and amperage the power supply can provide to the amplifiers, and there is a finite amount of power the amplifiers can deliver to the speakers. If we assume the 60 watt per channel figure is correct, then yes, with only two speakers connected, your receiver will only produce a maximum of 120 watts. But if you have all five speakers connected, and listening in stereo, you are still "missing" 180 watts.
The thing you must understand is the equation "watts = quality" is wrong. If the amplifiers do not clip, you have enough power.