By the same token, even though conclusions about the construction of the pyramids are arrived at inductively, that doesn't mean they aren't testable. After examining the evidence, I conclude that the Egyptians were able to levitate blocks of stone by chanting a particular verse and waving a dead chicken over them. So I chant the chant and wave the dead chicken, and sure enough, they don't levitate. So I've tested my hypothesis and falsified it - even though I wasn't there, I can disprove the chicken chant theory of pyramid origins.
So, maybe I take a closer look at the evidence to formulate another hypothesis about the construction of the pyramids. And given that I find large camp sites near the pyramids, with food storage and bakeries and so forth, large enough to support thousands of men, and that the stones themselves have marks consistent with stoneworking tools, I hypothesize that the pyramids were built over a period of time by many thousands of men, using the tools which we know from excavation were available to them.
But I wasn't there to observe the actual building of the pyramids - can my theories on the construction techniques of the Egyptians be tested? Can we know whether it was possible for them to have built it in the way I hypothesize?
From what I understand, there were not just "large camp sites" near the pyramids; there was a fairly good-size town there. Meaning there was an extended period of settled habitation in the area. I gather the burial site of a chief logistical officer -- a kind of "quartermaster" -- has recently been found, with exhaustive records regarding food, supplies, etc., etc. So we know there were thousands of people living at the site over a long time period in what was pretty much a permanent settlement.
But the question remains: What, exactly, were they doing there? Were they out there raising and rolling stones (some of which have been reported to weigh in at upwards of 15 to 20 tons) along a steep incline UP the pyramid, placed on logs and pulled along by a vast team of humans.
Now, can we estimate how many humans it would take to do this? -- to raise the 15+-ton stone, put it on log rollers, and drag it uphill until it could be set in its desired position? Plus we don't really know how the stones were brought to the site (floated on barges down the Nile seems a tad unrealistic, given the weight of these stones), or where the timbers came from.
I have read that even our currently-available, state-of-the-art, high-tech lifting devices (cranes) would not be able to accomplish all this, today.
Now, if indeed the construction method explained to us by the archeologists is, in fact, an impossibility, then what were all those people doing there? Clearly, as you note, this was some kind of work site. But what was the nature of the work?
Here's a what-if: What if the pyramids were already there, and were merely being refurbished to make them fit to receive the immortal soul of the pharoah? Just refitting marble facing stones all over the pyramid surfaces would have taken decades to accomplish. Plus perhaps the inner chambers would have needed to be refurbished to make the pharoah's final earthly resting place suitable to his needs. The Egyptians would have wanted a very secure location, beyond the reach of looters, for his mortal remains, plus all the royal accoutrements and appointments to which he had become accustomed in life -- perhaps including royal barges, furniture, etc., etc. The pyramids would be highly desirable sites for this purpose, from a security standpoint.
Anyhoot, that could explain what the Egyptians were doing there, in conformance with the evidence we have; but NOT how the pyramids got built in the first place.
I'd say: We still don't know that. It remains a great, enduring mystery....
General, you wrote: "Can we know whether it was possible for them to have built it in the way I hypothesize?" To which I would reply: YES. The hypothesis is -- as far as I can tell, based on the above -- incorrect.