People of African ancestry usually have only one alpha globin gene deleted per chromosome. The parents each have the mild thalassemia that results with two functioning alpha globin genes. The offspring can, at most, inherit the relatively mild condition of the parents. The answer is yes. Most large hospitals and clinics can perform routine hemoglobin electrophoresis.
Smaller laboratories send the test to commercial firms that can do the testing.
The DNA test for alpha thalassemia must be sent to one of the specialized laboratory facilities in the country. If you are concerned about the possibility of having thalassemia trait, you should speak with your doctor.