" by turning the volume all the way up?"
If one turns the volume all the way up, there is a good likely hood that the amplifier will be driven into clipping, depending on the level of the signal driving the amplifier.
In general this is not something that you want to do. Basic amplifier testing for repair purposes can be accomplished at less than full amplifier power. For amplifiers that require testing at full output power, then additional test equipment is needed.
Depending on the depth of the testing being done, when testing for maximum power output, one usually employes an oscilloscope, low distortion signal generator, a distortion meter and of course suitable dummy loads.
And as gadget73 mentioned, ideally one would want to use non inductive resistors for the output load for the amplifier.
The wattage rating of the dummy load is the maximum power that it can handle, not the amount of power that will be drawn from the amplifier under test by the dummy load. So using a dummy load with a higher power rating is acceptable. The amplifier under test will only produce the power that it is capable of producing and will not try to produce the rated power of the dummy load.
The power rating of the dummy load resistors is determined in part by how efficiently the resistor is able to shed, or radiate heat. This is intern in part determined by the physical size of the resistor. For example a 10 watt resistor is physically larger than a 1 watt resistor.
The point is that some of the cheap Chinese and other cheap power resistors are appreciably smaller than major brand resistors. This results in the resistors operation at a much higher temperature. Especially if the dummy load resistors are operated near their maximum power rating. This might lead to the unexpected failure of the dummy load resistor and this might not be a good thing for the amplifier under test.
Here is a link to
a recent AK thread that discusses power resistors.
For me it is a matter of being safe rather than sorry, although I know a number of people that have used the cheaper, physically smaller power resistors without issues.