I have followed the Atkins WOE both on and off oral contraceptives, and though I will admit the weight came off faster off the pill, I have still been able to lose weight while on the pill as well. It is possible. Like you, I was also placed on the pill by my doctor as an aid in managing my anemia because my periods were very heavy and i was not producing enough RBC's to stay in the normal range. I do also use them to prevent pregnancy though. So giving them up right now is not the best option for me.

Whatever you decide, I don't think your time on induction has been wasted. As Lisa said, some people do not experience a loss on induction. BUT induction is supposed to be a period of cleansing, when you rid your body of toxins, overcome your carbohydrate addictions, and convert to burning fat for fuel. If you've done this, then you've succeeded.