If hemoglobin and hematocrit levels are low, will platelet level also be low?

Not always: But if low hb, low hct are associated with low platelet , the it needs to be more evalauted as the conditions could be contributed by us such as alcohol use , or conditions of the bonemarrow from defective synthesis of precursor cells -called myelodysplastic syndrome, a bm failure blood has 2 types of cellular elements-red blood, white blood and platelets and their precursors come from bone marrow.