Yes it would, but that is not a description of ancient Egypt. Only the land for a few tens of miles on either side of the Nile was habitable. River traffic was policed (and taxed). And where did you get the idea that ancient Egypt was lightly populated?
Imagining that Egypt could be run as a gigantic slave camp is bizarre.
But we are discussing a Pyramid building site.
Now, about how populated Egypt was in those days, I'd guess anywhere from 500,000 to 2,000,000 total population on an annual average basis from the founding of the second kingdom right down to roughly the founding of Sparta in Greece. That's when Greece had a runaway population surge, due mostly to technological improvements and an improved variety of olive tree (and probably some other crops). Egypt shouldn't have been immune from that pressure.
Disease was big time back in the day. When Napoleon arrived they estimate the total population was about 3,000,000!
Here's a piece on it: http://www.reshafim.org.il/ad/egypt/people/index.html
BTW, almost forgot, the current population of Egypt is about 82,000,000. That’s about 40X the population of the period we are talking about ~ a far different society!