I am not a biologist but I can give you some of my problems with the idea.
I'll just give a couple of quotes from the Wikipedia page. For starters it an error to believe that this 'Mitochondrial eve' was the only female alive at that time.
"One misconception surrounding mitochondrial Eve is that since all women alive today descended in a direct unbroken female line from her, she must have been the only woman alive at the time. However, nuclear DNA studies indicate that the size of the ancient human population never dropped below tens of thousands. Other women living during Eve's time have descendants alive today, but at some point in the past each of their lines of descent did not produce a female, thereby breaking the mitochondrial DNA lines of descent"
And of course to accept the existence of Mitochondrial eve is to also accept the principles of evolution as it's existence and
Another is frankly the estimated age of this character which is grossly inconsistent with the time frame in the bible.
"Mitochondrial Eve is estimated to have lived between 99,000 and 200,000 years ago, most likely in East Africa, when Homo sapiens sapiens (anatomically modern humans) were developing as a population distinct from other human sub-species."
And finally to accept Mitochondrial eve is to accept evolution, to use such an idea which is absolutely dependent on the idea of evolution to prove the bible is just absolutely contradictory.