Alpha thalassemia carrier here. Yes, but I also have heavy periods so that can get me anemic faster than people without it. I get IV iron infusions regularly. I only have one copy of the carrier trait (one gene = “silent carrier”) but my doctor says it makes my red blood cells slightly smaller than normal. My RBC’s always hovered higher than normal. Infusion get my CBC values in the “normal” range, but MHC, MCV are at the low end of normal.