[FrankenPC]

OK. So, the great pyramids were nearly 500ft tall. At the top, the pressure below would have been around 200psi. Even the most stalwart modern plumbing fixtures have trouble past 72psi. 100psi is the upper limit before things start to fail. I don't think that there would be a mechanical problem with stone holding back that pressure, it's the leakage that would be the killer.

[maxerickson]

Modern plumbing stuff is designed to be economical. (Which just limits the usefulness of extrapolating from there)

If the mechanics of using the stonework to hold the water were well worked out I would think clay would work well to seal small cracks (and for the scale we are talking about, the 'plumber' could just crawl on in). Or pitch or other sticky stuff.

[mekoka]

The theory mentions multiple shafts, not a single contiguous one.