Should depleted iron stores always correlate with low hemoglobin or are they not affected by each other ?

Hemoglobin has iron: Low iron levels reduces hemoglobin and changes its structure. Elevated iron doesn't increase hemoglobin past a certain point, it just gets deposited into tissue and organs.

Very much related: Iron is necessary for the appropriate formation of hemoglobin. So if you have low iron levels, you'll likely have low hemoglobin levels. Realize there may be a bit of a lag/delay between when your iron levels reach a threshold that manifests as low hemoglobin levels.

Not always.: Some people have iron deficiency without anemia. Symptoms from iron deficiency anemia can occur with iron deficiency alone with anemia.