If someone has iron deficiency, and they got a physical and drew blood, would their test results show this?

Only if they specifically test for anemia.

Yes, the blood work for a physical will include all of the very basic things like iron count, white blood count, red blood count and so on.

you would see it for sure

It would show anemia (low hemoglobin) since it would measure hemoglobin levels, but not what caused it. But if your hemoglobin is normal, you don't have iron deficiency.

Iron deficiency will be demonstrated only by lab tests and clinical exploration. This last will be done by the physician and he could suspect iron deficiency by means of anemia data. The lab test to detect iron deficiency are: Red blood cell (RBC)count and their parameters, hemoglobin determination, serum iron, total iron binding capacity and ferritin levels. Usualy the  RBC results are abnormal until the iron deficiency is important. Hope this outline being helpful.

Iron deficiency anemia is diagnosed based on several parameters including: hemoglobin levels (normal for men 13-17g/dl or women 12-16g/dl), size of the red blood cell (typically small or microcytic in anemia) and iron studies (ferritin, transferrin, total iron binding capacity (TIBC), reticulocyte count and RDW (red cel distribution width).
If you  had a physical, they typically just draw a CBC which provides the white blood cell count, red blood cell count, RDW, hemoglobin and platelet count.  Based on the CBC you can suspect an iron deficiency but you have to confirm it with iron studies (see above description).
Hope this helps.

Iron deficiency shows up in laboratory testing as low hemoglobin (the major iron-bearing/oxygen-carrying protein in the blood),  low hematocrit ( low volume of cells per fluid), low MCV (average red cell size). Also, directed tests for ferritin (another iron carrying molecule) and total iron could be measured.
Old Doc

The iron deficiency tests can be false or more exact misleading!! If you are of mediterranean descent you can have LESS red blood cells which indicate anemia BUT have MORE in quantity which is not picked up by the doctors as a rule!!! result -no anemia!!!! Iron supplementation can be dangerous due to its toxicity !!There have been deaths from irresponsible recommendations for iron supplementation !! Therefore be wary and make sure the doc knows about the mediterranean type of so called anemia!!!!