For those who are not transsexual, the answer is generally yes. But for those in the part of the transgender population who feel the need to bring their anatomy in line with their deeply held belief of being the opposite gender, this is a challenging question that's increasingly important.
Heightened awareness to and sensitivity toward all transgender people is resulting in younger and younger gender transitions. And the desire of younger transsexual people to become parents can be just as strong as for those who are not transsexual. But it presents a fairly significant challenge.
For a transsexual woman (assigned male at birth), genital surgery generally gives her a functional vagina constructed from her prior genitalia. It does not, however, give her ovaries, a uterus or a cervix. Medical science is far from being able to transplant those female reproductive organs for anyone, trans or not.
For a transsexual man (assigned female at birth), genital surgery generally gives him male genetalia that can sometimes be used for sex. It does not, however, give him functional testicles, and doctors are far from perfecting transplants for them, too.
These considerations are often missed by policymakers who set genital reconstructive surgery as a requirement for changing the gender marker on an identity document. GRS generally removes the ability to reproduce via conventional intercourse, and its exclusion of GRS from most employer health insurance coverage renders it unaffordable for many.
Much as non-transgender people who cannot conceive are resorting to creative means to bring a much-desired child into the world, so are transsexual people. For my information on this, I am relying on one of the best resources available for parents of transgender children, "The Transgender Child: A Handbook for Families and Professionals" by Stephanie A. Brill and Rachel Pepper.
For those needing to transition now but wanting to preserve the option of having biological children, both sperm and eggs can be banked for later use. When it later comes time to have children, one can choose to do so through assisted reproduction services with their female partner, or through engaging the services of a traditional or gestational surrogate. These are approaches also used by non-trans people.
Some transsexual men may still have female reproductive organs, either because they were unable to afford the cost of their removal, or because they may have chosen to maintain them "to keep their options open."
Yet bearing a child after being on testosterone therapy is not without risk. One is generally able to conceive and carry children about 18 months after stopping testosterone therapy, although there is no guarantee that the reproductive system will still function correctly. Trans men on testosterone treatments often have an elevated risk of developing polycystic ovary syndrome (PCOS), which usually causes infertility. There are also increased risks of birth defects after lengthy testosterone therapy.
A more pragmatic problem with this approach is that testosterone therapy will have already caused facial hair growth and lowered the voice, effects that are not reversible. You will thus appear to be a "pregnant man," the label given to Thomas Beattie when he received worldwide attention for carrying his child. The other trans men who have taken this route to have their own children have been more secretive in doing so.
Transsexual women, on the other hand, may still have male reproductive organs, either because surgery was unaffordable or to preserve reproductive options. For those desiring children, stopping estrogen therapy for a period of time may allow sperm production to resume, although it may not be at a sufficient level to produce a pregnancy without assisted reproduction, if at all.
The pragmatic challenge in this case will be that, without estrogen, facial hair may resume growing and breasts will shrink a bit, two things that are difficult for any woman to accept. For that matter, so will be going to sperm bank as a woman to store, rather than obtain, sperm.
Now, consider the additional challenges facing parents of transgender children. A child may be devastated when puberty arrives, bringing with it the prospect of a low voice and male facial features for those who believe themselves to girls, and breasts, menstrual cycles, and short stature for those who feel they are boys. These "secondary sex characteristics" are the features most likely to cause others to fail to perceive the child as a member of their gender.
Parents may respond now by placing the child on medications to block puberty before later allowing the child to begin cross-hormone treatments. But without having gone through natal puberty, anatomical males will not produce sperm and anatomical females will not have eggs capable of maturing for fertilization. Yet since natal puberty can resume normally as long as the blocker is stopped by age 16, some parents will feel safe following this course.
The much harder decision comes if the child insists on having genital reconstruction surgery. Ignoring the fact that surgeons almost never perform GRS on a patient under age 18, GRS before natal puberty essentially eliminates the ability of a child to produce their own biological children. This is an agonizingly hard prospect for most parents to accept.
So while there will likely be increasing numbers of "out" transgender children in the coming years, those who base policies on anatomy will need to be prepared for the fact that most of these children will not yet have had genital surgery.