It depends. That single part of a story is in itself possible.
For instance, if we were to hypothetically take a fertilized egg, with 23 pairs of chromosomes (including 1 X and 1 Y), and remove the Y, double the X, and let things gestate from there, then yes, we'd get a female version of what would have been a male.
Or, if cloning were possible, we could take the 23 pairs from a man, remove the Y, double the X, and gestate that to term, providing a female clone of the male.
However, taking that as an Adam and Eve origin runs into all kinds of problems compared to what we know now. (and, most of these problems also apply to all ideas that have a total population of 2 at any time in the past 50,000 years). For instance, consider alleles. Alleles are different varieties of a gene - so for a gene that codes for eye color, two different alleles could be "brown eyes" and "blue eyes". In your clone situation, Eve is a copy of Adam, and hence has the same alleles for a given gene. Even if Adam had two different alleles there (the maximum possible since we all have two copies of each gene), then there could be a maximum of 2 different alleles in the gene pool.
For instance, ABO blood type is based on three alleles: A, B, and o. (remember that everyone has two copies of each gene). o is recessive, so AA, or Ao give type A, BB or Bo give type B, AB gives type AB blood, and only oo gives type o blood. So you can't get our current situation from an Adam clone, since his two genes can't cover the three alleles we have.
In fact, many genes have many more than three alleles found in the population. Many have dozenes of alleles, some have over 100.
Bottlenecks - which is when a population goes below a few dozen thousand individuals - show up clearly in DNA - that's how we know of bottlenecks in the history of, say, cheetahs. Genetic studies of many other areas of the genome show that humans went through a moderate bottleneck (down to a few thousand people) sometime around 50,000 years ago (Toba). An extreme bottleneck of 2 people - or just one in your Adam/Eve clone idea, would be very obvious, and would date to ~6,000 years ago. Yet, that's not what is seen.
There are many other reasons that we know the breeding population of our ancestors never went below about 1,000 any time in the past 100,000 years. All of them show that both the 2 person and your new 1 person ideas don't fit the data. But, at least your 1 person idea is no worse off than the standard creationist 2 person idea.
In Christ-
Papias