Fabulous question!
I have been in the Consumer Electronics Industry since 1992 and have owned a high end retail store, worked as a rep, and now for a wonderful Amplifier and Speaker Manufacturer. Having dealt with engineers and industry insiders directly for that amount of time, I feel I more than qualified to be an authority in answering this.
Just like a car, without question, there is a "Break-in" period on everything and if you are a denier of cars actually having a "breaking-in" period, then there is probably no way to have a rational conversation about any of this...
Different things have different break-in periods and no two things are alike. However, just like with cars, you reach a point where you get what you get in relation to gas mileage and how the car reacts and works. Electronics, Speakers, Cables, all of it, have that point.
So the quick answer to the question is; how much volume you put through the system does NOT matter at all! What matters is putting a signal through everything and simply playing it with no need to overthink this here. If you can hear sound coming from your speakers, everything is breaking in.
With electronics, particularly DAC's and Preamps, each input has it's own break-in time and you need to have a signal running through all of it. The only time you need to physically hear something from the speakers is if you're breaking in speakers and amps. Or, you can put a resistor on the output of the amps to break those in if needed, but you have to have a signal going in and physically going out for full "break-in".
These are all good things to know when visiting dealers, because in today's world, where foot traffic isn't what it used to be, there is a lot of equipment on dealer's showroom floors that may have been setting there for a year and still haven't been played enough to where the equipment is fully broken in.
So, what's the magic number for length of time? Like I said, everything in the chain is different, but I know with our products that number is 300 hours. That's twelve and half days of solid play 24/7 because we can physically hear it and as a team, we have all collectively come to that consensus. I can walk into one of our dealers and play our equipment and know right away the moment I play something when that the equipment has not had a significant amount of time on it. That just comes from experience of doing this ALL THE TIME!
Other manufacturers may require more or less time and people who work for those companies or sell those products should know what that amount is. In the case with Audio Research, some of their amps, they are actually recommending 600 hours of break-in. Who cares what the amount of time is, just play the stuff and I guarantee you'll hear it change.
The last thing is, some products are good out of the box and can actually get worse as you play them, only to come out of the hole and get better after a certain period of time. We have amps that do that and I will also point to older 300 Series amps from Mark Levinson (No.331, 332, 333, 33H's, and 33's) were all like that back in the day when they were new. They were pretty decent out of the box and got so bad at about 100-150 hours that we thought they were broke, and then they climbed out of the cellar and got great.
So in conclusion, I hope this answers and clears up most of this for some or all of you? I realize that there will always be skeptics out there, but until you work in this industry and are around equipment as much as we are, along with getting insight from the people who are involved in building it, you'll just continue to believe what you want - and that's ok! I've said what I believe to be true and have no problem sleeping at night over what I've shared here.
Thank you all for your time in reading this.
Chris