Yes the woman still produces eggs, but the sperm cannot reach to fertilize it because there isn't a uterus to travel up. Your eggs could probably be harvested if you see a specialist, and be fertilized in a test tube per se. Then implanted into a woman with a uterus.
If the woman did not have one or both of her OVARIES removed during the hysterectomy, then she DOES still OVULATE. This is done when the woman or her Doctor prefer to maintain her natural hormones, instead of HRT. (Hormone Replacement Therapy) The egg, once ovulated, is absorbed by the body, thus providing the natural hormones.
I am doubtful that eggs could be harvested once a hysterectomy has been performed, as the cervix, uterus, and tubes (and often the ovaries) are now gone. (However, I am not a doctor.)
This is a decision that should be made PRIOR to the hysterectomy, if harvesting of eggs is being considered.
