Can the third sex be categorized as Male or Female?
When dealing with humans, there are only two Biological genders as defined by the presence or absence of the Y-Chromosome. If the Y-Chromosome is not present, or through some process gets totally deactivated, the human will appear and function as a Female.

XX = Female

XY = Male

XXY = Male (Klinefelter's Syndrome)

XYY = Male (Aneuploidy - Normal Functioning Males)

XXX = Female (Aneuploidy - Normal Functioning Females)

X = Female (Turner's Syndrome - Generally infertile, other issues)

Y = Fatal (The Y-Chromosome is drastically smaller than the X-Chromosome, which contains many necessary genes)

XXYY = Male

...

The list goes on, since there have been records of up to XXXXX.

If there is a Y-Chromosome present, the human born will be male.

However, that is not to say that a person cannot psychologically identify as something else. It's also worth noting that the majority of known species are asexual and do not have genders, and that those which do have genders do not always follow the same rules (Fruit Flies, for instance, use the ratio of genes to determine sex).