Is it normal to be constantly tired while pregnant?

Yes. Feeling fatigued during pregnancy is common, especially in the 1st and 3rd trimesters. Although many women have more energy mid-pregnancy that is not always the case. Before accepting constant fatigue as normal, you should discuss with your caregiver and make sure medical conditions such as anemia, thyroid disease, and diabetes have been ruled out and that you are eating and sleeping optimally.
Depends how tired. I am sure you have spoken to your OB because your OB would want to r/o things like anemia, thyroid under function, viruses, etc.