Higher voltage and current through the cables would accelerate the break-in, so the basic answer is yes, to an extent. So, what do you do about the noise?
You can connect BIG power resistors instead of speakers. They will get very hot if you're running 10W or more, even if the resistors you buy are rated for that power level. For levels above 10W you should consider metal-encased resistors with a heat sink and perhaps even a cooling fan.
If you don't want to put hours on your precious amp, then buy a high-power receiver from a thrift store and tune it between FM stations with the mute off. The white noise is a pretty decent burn-in "program" material!
Turn the volume up slowly and monitor the temperature of the power resistors as you do that. Heat build-up in large resistors is quite slow, so give them a few minute with each step of the volume control.
Another method is to connect the speaker cables as power cords for a high power appliance. I cannot recommend this method to anyone that is not familiar with electrical installations safety requirements.
Last comment... IF your spakers are new, they will need a serious burn in and there is no way around that noise issue. :-(
Some burn-in CDs have subsonic and ultrasonic material, which lowers the perceived exposure to noise, but it's inevitable. The midrange drivers must be "moved" and the only way to do that is with audible tones.