Here's a complete answer.
No
Because sex is defined as "either of the two main categories (male and female) into which humans and most other living things are divided on the basis of their reproductive functions."
Male is defined as "of or denoting the sex that produces gametes, especially spermatozoa, with which a female may be fertilized or inseminated to produce offspring."
Female is defined as "of or denoting the sex that can bear offspring or produce eggs, distinguished biologically by the production of gametes (ova) which can be fertilized by male gametes."
So sperm producers are male and ova producers are female. But some people are sterile, so for people who produce neither sperm nor ova, what does it mean to be 'of the sex' of one or the other? Lets take a look at biology. Ova only come from ovaries. Testes never produce ova. Sperm only come from testes, ova never produce sperm. No one has ever had a gonad that produced both sperm and ova, nor one of each. No one has ever changed from being a sperm producer to an ova producer or vice versa.
So we can say if you have ovaries you are female, if you have testes you are male. That's definitely in the same reproductive category. But what about people who, for whatever reason might be born with neither? It's extremely rare but lets look at how humans develop.
In the uterus, two gametes (sperm and ovum) come together to make an embryo. In the beginning that embryo has undifferentiated gonads, which could be either testes or ovaries. If the person has an SRY gene (almost always on the Y chromosome) those gonads will differentiate into testes. If they do not, the gonads will differentiate into ovaries.
At its most fundamental level, sex is determined by the presence or absence of the SRY gene, which directly controls differentiation of the gonads, which in turn determines which part of the reproductive act the person could hypothetically take part in (sperm producer or ovum producer) and USUALLY results in specific hormonal production and sexual characteristics that we are visibly able to recognize in a person as male or female.
As presence or absence of the SRY gene is a binary characteristic there are only two sexes, no one is both, no one is neither, and no one can change from one to the other. Sex is encoded in every cell of your body and is a fundamental part of your body's operating system.
So anyone with XY, XXY, XXXY or XXmale (where the SRY gene is present on the X chromosome) genotypes is male. Their gonads will differentiate into testes. They MAY produce sperm. They will usually be phenotypically male. They will never have ovaries or produce ovum. This includes men with CAIS and other intersex conditions.
Anyone with X, XX, or XXX genotypes is female. Their gonads will differentiate into ovaries. They MAY produce ovum. They will usually be phenotypically female. They will never have testes or produce sperm. This includes women with CAH and other intersex conditions.
Some sexual characteristics can be changed (breasts or penis can be removed) but sex itself can't ever be changed.