Could a trans-female person ever become pregnant?
Medical science has reached the point where it is able to consider performing uterine transplants in genetically female (cis-female) patients born without a uterus.
In the MedlinePlus report, First Uterus Transplant Planned in U.S. doctors at The Cleveland Clinic have plans to perform the first uterus transplant in the US sometime in 2016.
The article does however go on to state that the women will need to have been born with ovaries. The same matching process of blood and tissue typing that goes along with any organ transplant would still be in effect for this surgery.
It is also unlikely that the procedure would be open to women that lost their uterus due to cancer, as the recipients would be required to be on immunosuppression medication, and the risk of cancer recurrence would be too great.
As for your question about transplantation into Male-to-Female transgender patients, it is unlikely, at least with present technology that the person would be able to receive the transplant. There is a complex cascade of hormone signaling required for implantation of the embryo.
There could also be implications as to the formation of the placenta and how the person's body react to that. We have many examples of surrogacy, so we know that a woman can carry the embryo formed from the egg of another woman, but how the transgender person's somatic cells would react, given that they all have y-chromosomes is unknown.
According to a Yahoo! news article that interviewed Dr. Karine Chung, director of the fertility preservation program at the University of Southern California’s Keck School of Medicine and Dr. Christine McGinn, a New Hope, Pa., plastic surgeon who performs transgender surgeries on men and women, they foresee possibilities that this could happen in the future, however they do not cite any research that has been performed to date.
One of the issues would be the differing pelvic vasculature that a cis-male has to a cis-female, and what would need to be done to provide an adequate blood supply to sustain not only the uterus but the growing fetus as well.

...biological women have a leg up on biological males when it comes to accepting and nurturing a transplanted uterus. Women already have: vasculature needed to feed the uterus with blood, pelvic ligaments designed to support a uterus, a vagina and cervix, and natural hormones that prepare the uterus for implantation and support the pregnancy.
Men have none of those support systems — naturally — but none are impossible to create. “Male and female anatomy is not that different,” says Chung. “Probably at some point, somebody will figure out how to make that work.” (2)

The article does go on to point out that


Hormone therapy can shut off testosterone and introduce progesterone and estrogen needed to prepare the uterus for pregnancy.

Even though males do not have uterine veins and arteries needed to nurture the womb, it’s possible to attach a branch of a large vessel, like the internal iliac, to the uterus. “It’s doable, it just hasn’t been done,” Chung says.

Although it’s preferable for a vagina to support the uterus, it’s possible to attach a transplanted uterus to other ligaments in the pelvis.