To be clear, there are lots of ways we can look at human / sex gender, and there are lots of variations to occur. Nothing is any less real about people when their parts don't match, rather it be their DNA or their genitalia. These people may not be the majority, but they are no less real. And due to these variations there have been many attempts to define human sex. One attempt has been to look at DNA, the XX/XY genes which many people are familiar with. This is the XX/XY sex-determination system, but it isn't actually used and here is why:

If you were to take a DNA swab of any woman, what sex would the DNA results tell you? And after that, what relevance does it have to her being a woman, to her sex/gender? It is a false conclusion that DNA is relevant to the relationship, sexual attraction, or the determination of gender/sex. There are all sorts of genetic variations in women. Geneticists don't use chromosomes to determine sex/gender in people. It isn't known to be an accurate indicator. Genes are just a map, or a plan even. It doesn't mean that the plan is followed.

Phenotype is a far more determining factor of sex/gender than DNA (edit: or any other single factor) ever will or could be.

We don't karyotype people with our eyes or beliefs, contrary to some claims. What relevance does someone's DNA have on their sex/gender/appearance/etc? Everything you see and interact with about a person can be completely opposite of what their genes tell you should be reality. For the majority, their chromosomes may be in line with what you see. But that doesn't prove anything about the relationship between DNA and sex/gender. There are plenty of women, trans and otherwise, that do not match. (Men too for that matter.) There is such thing as an XY woman.

Also sex/gender is far more than just chromosomes. Neurology plays an extremely important part, and that is the part that does not match in trans people. Neurology is going to form the foundation of your identity/gender. And neurology is the component of trans women that does not match (possibly) their DNA. In real life, when people do gender tests, it takes a wide range of doctors/specialists to make the determination. And it should be noted that the medical community accepts the validity of transsexuals as women.

Gender verification tests typically involve evaluation by gynecologists, endocrinologists, psychologists, and internal medicine specialists. As you can see, there is far more to gender/sex than genes. Making that determination isn't the job of geneticists either. Not to mention, it can be incredibly inaccurate even still.

http://en.wikipedia.org/wiki/Gender_verification_in_sports
Gender verification tests are difficult, expensive, and potentially inaccurate. Furthermore, these tests fail to exclude all potential impostors (eg, some 46,XX males), are discriminatory against women with disorders of sexual development, and may have shattering consequences for athletes who 'fail' a test.

DNA is an irrelevant piece of the gender/sex puzzle when it comes to sexual attraction as well (or any human interaction.) As I already pointed out, what people are attracted to (and what they interact with) is the person's phenotype -- "the composite of an organism's observable characteristics or traits: such as its morphology, development, biochemical or physiological properties, phenology, behavior, and products of behavior..." And that can obviously be changed in the case of a congenital neurological intersex condition, like transsexuality.

http://en.wikipedia.org/wiki/Phenotype Biological determinism (basically the idea that you are what your DNA says) is not an accurate view of humanity. In fact "Biologists sometimes regard a charge of biological determinism as a straw man, as there is currently no support for strict biological determinism in the field of genetics or development, and virtually no support among geneticists for the strong thesis of biological determinism. "http://en.wikipedia.org/wiki/Biological_determinism

So to conclude, "If I were to take a DNA swab of a transgender woman, what sex would the DNA results tell me she was? " It wouldn't. It tells you absolutely nothing. Edit: Phenotype is what is used in the determination of sex in human beings, and that includes everything from genitalia to endocrine system -- and even neurology. We're all real.

Here is more information for those that like to learn:
http://en.wikipedia.org/wiki/Causes_of_transsexualism
http://en.wikipedia.org/wiki/Transsexualism
http://en.wikipedia.org/wiki/Transsexualism#Causes
http://en.wikipedia.org/wiki/Causes_of_transsexualism#Brain_structure

Genitalia is not the single factor used to determine sex either: http://en.wikipedia.org/wiki/Gender_verification_in_sports http://www.isna.org/faq/

Total number of people whose bodies differ from standard male or female one in 100 births http://www.isna.org/faq/frequency There are all sorts of variations in humanity. We're all real.