I am skeptical that once you remove non-African ancestry from Egyptians (even if you were able to do so perfectly), what you are left with is indigenous Northeastern Africans, the direct descendants of people who left Africa tens of thousands of years ago.
For one thing, Egypt has not only experienced gene flow from Europe and the Middle East, but also from elsewhere in Africa, more recently because of enslaved black Africans.
For another, even if you perfectly identified and removed both Eurasian and African non-native influences on the Egyptian population, you're left with some kind of indigenous northeastern African. But, did such a population with long-term continuity exist in Egypt since Out-of-Africa? The Eurasian experience (where ancient DNA falsifies continuity left and right even in a 1/10th of the OOA time scale) makes me doubt this. The Nile may have facilitated gene flow in a north-south direction, and the relatively recent emergence of the Sahara desert may very well have pumped populations into Egypt.
AJHG DOI: http://dx.doi.org/10.1016/j.ajhg.2015.04.019
Tracing the Route of Modern Humans out of Africa by Using 225 Human Genome Sequences from Ethiopians and Egyptians
Luca Pagani et al.
The predominantly African origin of all modern human populations is well established, but the route taken out of Africa is still unclear. Two alternative routes, via Egypt and Sinai or across the Bab el Mandeb strait into Arabia, have traditionally been proposed as feasible gateways in light of geographic, paleoclimatic, archaeological, and genetic evidence. Distinguishing among these alternatives has been difficult. We generated 225 whole-genome sequences (225 at 8× depth, of which 8 were increased to 30×; Illumina HiSeq 2000) from six modern Northeast African populations (100 Egyptians and five Ethiopian populations each represented by 25 individuals). West Eurasian components were masked out, and the remaining African haplotypes were compared with a panel of sub-Saharan African and non-African genomes. We showed that masked Northeast African haplotypes overall were more similar to non-African haplotypes and more frequently present outside Africa than were any sets of haplotypes derived from a West African population. Furthermore, the masked Egyptian haplotypes showed these properties more markedly than the masked Ethiopian haplotypes, pointing to Egypt as the more likely gateway in the exodus to the rest of the world. Using five Ethiopian and three Egyptian high-coverage masked genomes and the multiple sequentially Markovian coalescent (MSMC) approach, we estimated the genetic split times of Egyptians and Ethiopians from non-African populations at 55,000 and 65,000 years ago, respectively, whereas that of West Africans was estimated to be 75,000 years ago. Both the haplotype and MSMC analyses thus suggest a predominant northern route out of Africa via Egypt.