This is not really correct. Far and away the biggest genetic analysis of Ashkenazim was published in 2013, and has rather conclusively shown that the great majority of maternal DNA contribution in Ashkenazim was from European stock, with the men being Middle Eastern. So it seems that the Ashkenazim primarily derived from a mixture of male Jewish immigrants and female European converts, starting with a fairly small founding group.
http://www.nature.com/ncomms/2013/131008/ncomms3543/full/ncomms3543.html
Overall conclusion: "Therefore, whereas on the male side there may have been a significant Near Eastern (and possibly east European/Caucasian) component in Ashkenazi ancestry, the maternal lineages mainly trace back to prehistoric Western Europe. These results emphasize the importance of recruitment of local women and conversion in the formation of Ashkenazi communities, and represent a significant step in the detailed reconstruction of Ashkenazi genealogical history."
As to whether they comprise a 'race,' that word gets thrown around loosely ... they don't comprise a discrete population that is readily identifiable amongst all others by phenotypical traits. But they do represent a concentration of certain genetic traits, albeit very loosely integrated with European genetics. Part of that is due to 'bottleneck' effects that happened to Ashkenazim genetics at very times, however, concentrating them after the initial intermixing with European genetics. More colloquially, inbreeding, which followed the initial outbreeding. There was a MASSIVE bottleneck a mere 700 years ago, where basically a mere 300 or so Ashkenazim contributed almost all of the genetics that multiplied into the modern Ashkenazi gene pool.
http://www.theoccidentalobserver.ne...ews-following-medieval-population-bottleneck/
There used to be a ton of pretty dubious genetic analysis of these issues, going back and forth, but with these recent papers it looks like the data has finally gotten quite good.
Your evidence is backed by some data, but alternative sources claim opposing views:
http://www.ftdna.com/pdf/43026_Doron.pdf is the source for the below:
A 2006 study by Behar et al.,[55] based on high-resolution analysis of Haplogroup K(mtDNA), suggested that about 40% of the current Ashkenazi population is descended matrilineally from just four women, or "founder lineages", that were "likely from a Hebrew/Levantine mtDNA pool" originating in the Middle East in the 1st and 2nd centuries CE. Moreover, a maternal line "sister" was found among the Jews of Portugal, North Africa, France, and Italy. They wrote:
Both the extent and location of the maternal ancestral deme from which the Ashkenazi Jewry arose remain obscure. Here, using complete sequences of the maternally inherited mitochondrial DNA (mtDNA), we show that close to one-half of Ashkenazi Jews, estimated at 8,000,000 people, can be traced back to only four women carrying distinct mtDNAs that are virtually absent in other populations, with the important exception of low frequencies among non-Ashkenazi Jews. We conclude that four founding mtDNAs, likely of Near Eastern ancestry, underwent major expansion(s) in Europe within the past millennium...[13][55]
http://www.nature.com/ejhg/journal/v15/n4/full/5201764a.html is for the below:
A 2007 study by J. Feder et al.[56] confirms the hypothesis of the founding of non-local origin among the maternal lines. Their study did not address the geographical origin of Ashkenazim and therefore does not explicitly confirm the origin "Levantine" of these founders. This study revealed a significant divergence in total haplogroup distribution between the Ashkenazi Jewish populations and their European host populations, namely Russians, Poles and Germans. They concluded that, regarding mtDNAs, the differences between Jews and non-Jews are far larger than those observed among the Jewish communities. The study also found that "the differences between the Jewish communities can be overlooked when non-Jews are included in the comparisons." It supported previous interpretations that, in the direct maternal line, there was "little or no gene flow from the local non-Jewish communities in Poland and Russia to the Jewish communities in these countries."[57]
See also, from
http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1004401 :
A 2014 study by Fernandez et al have found that Ashkenazi Jews display a frequency of haplogroup K which suggests an ancient Near Eastern origin, stating that this observation clearly contradicts the results of the study led by Richards which suggested a predominantly European origin for the Ashkenazi communities.[62]
The text/sources above were drawn from the wikipedia article on this subject, with direct links to the source material.
What are we to draw from these contradictory conclusions?
A few potential things:
1. Ashkenazi interbred with European (potentially Italian) women about 2000 years ago, and have since kept to themselves.
2. The European identity of these haplogroups is misconstrued, as the same haplogroups are found also in the ME.
3. The Jews have widely interbred with European peoples in the period between 100-2000 AD.
I think the third is ruled out by history, and 1 and 2 are reasonable hypotheses.
Conversely, the paternal ancestry is definitive: These Jews are Jews. They are semitic, Middle Eastern in origin, and often carry the same y-chromosome across important priestly distinctions.
So, are Jews a "race"? No, though they are likely to be considered a sub-race of the family/sub-race of the Caucasoid race that are the Semitic peoples.