First off, the pharmacist concern is with the iron binding with the abx and thus having the abx not be effective. However, depending upon how often the abx are taken, it may be possible to still take the iron. The iron should be taken at least 2 hours away from the abx. Also, you should ask your doctor about giving probiotics when your son is on abx. That will help replenish the healthy bacteria that are also killed when he takes the abx.
It takes quite some time to bring iron levels back up (I hope your doctor is also measuring the ferritin as that's the most accurate measure for iron stores), so that's likely why the pharmacist is suggesting to wait to start the iron until the abx are done.
As far as the CBC results, our family has dealt with the same issues (low WBC and both B vitamin and iron deficiency anemia) and it was not leukemia. The reason your son is getting pneumonia and other illnesses so frequently is because the WBC is so low, his body is not able to adequately fight the infections.
If you look at some of the info you find online as far as what causes a low WBC, one of the things listed is autoimmune diseases/inflammatory diseases. My family has all been diagnosed with celiac disease (believed to be one of the root causes of all autoimmune disorders). Iron deficiency anemia is also a primary symptom of celiac (I had that at age 6 and unfortunately wasn't diagnosed as celiac until I was over 40 - my sons were diagnosed at 8 and 11). So, I suggest you ask your doctor to screen for that - it is one of the most commonly under-diagnosed disorders today. There is no drug for the disease - it just requires you stay on a gluten-free diet. The reason this will have such a profound positive effect on your health is that the gluten damages the wall of the intestine so that nutrients and vitamins are not absorbed, thus your body gets into this state where there are so many random things wrong. For example, your body needs things like the amino acid Taurine and certain B vitamins to make white blood cells. And, of course, it needs the iron to make RBCs. CBC results can also be very misleading as B vitamin based anemia results in a high MCV and iron deficiency anemia leads to a high MCV. So, some folks with these problems actually won't be diagnosed appropriately.
I hope this helps.