

First graph: Distributions of Pairwise Sequence Differences among Humans, the Neanderthal, and Chimpanzees. X axis = number of sequence differences; Y axis = percent of pairwise comparisons. (Krings et al, 1997).
Second graph: Green: human/human comparisons; Red: human/Neanderthal comparisons; Blue: human/chimp comparisons. X axis = number of sequence differences; Y axis = fraction of pairwise comparisons. (Green et al. 2008)
The answer is ‘yes’ if we look at individual DNA sequences, as shown in the first graph (above):
Thus, the largest difference observed between any two human sequences was two substitutions larger than the smallest difference between a human and the Neandertal. In total, 0.002% of the pairwise comparisons between human mtDNA sequences were larger than the smallest difference between the Neandertal and a human (Krings et al., 1997)
It may be noted that a small fraction (0.037%) of the inter-human comparisons are larger than the smallest distance (29 substitutions) between the Neandertal and humans. (Krings et al., 1999)
We can likewise eliminate the overlap between Neanderthals and modern humans if we use the entire mtDNA genome to compare these two populations:
In 2008, the first complete sequencing of Neandertal mtDNA was announced (Green et al. 2008). A complete mtDNA genome of 16,565 base pairs was extracted from a 38,000 year old fossil from the Vindija cave in Croatia. As Krings et al. 2007 had done, the authors created a graph showing the numbers of base pair differences for humans, chimps and the Neandertal when compared against humans. Because they were able to compare across the whole genome rather than a small portion of it, the differences between humans and the Neandertal was far more striking (Fossil Hominids)
This may be seen in the second graph (above).
But why must we compare entire genomes to make the overlap go away? Why should there be any genetic overlap between two populations for any stretch of DNA if the same populations show absolutely no visual overlap to our lying eyes? What’s going on here?
The underlying reason is that most of the genome has little selective value. So the selection pressure on that DNA is pretty much the same in any population, be it Congolese, Danish, or Neanderthal. Of course, once two populations become reproductively isolated, i.e., when they become different species, their DNA will start to drift apart even at genes of low selective value (because of differing patterns of random mutations). But this divergence is very slow. Consequently, it is hard to distinguish between related species that have diverged from each other only over the last 40,000 years. This is why Neanderthals and modern humans still have some overlap, even though their last common ancestor lived over 400,000 years ago.
References
Fossil Hominids: mitochondrial DNA,
Green, R., A-S. Malaspinas, J. Krause, A. Briggs, et al. (2008). A complete Neandertal mitochondrial genome sequence determined by high-throughput sequencing, Cell, 134, 416-426.
Krings, M., H. Geisert, R.W. Schmitz, H. Krainitzki, & S. Pääbo. (1999). DNA sequence of the mitochondrial hypervariable region II from the Neandertal type specimen, Proc. Nat. Acad. Sci. USA, 96, 5581-5585.
Krings, M., A. Stone, R.W. Schmitz, H. Krainitzki, M. Stoneking, & S. Pääbo. (1997). Neandertal DNA sequences and the origin of modern humans, Cell, 90, 19-30.
Risch, N., E. Burchard, E. Ziv, & H. Tang. (2002). Categorization of humans in biomedical research: genes, race and disease, Genome Biol, 3, 1-12.
Sesardic, N. (2010). Race: a social destruction of a biological concept, Biol. Philos, 25, 143-162.