No! In the Nordic Guidelines, iron is recommended for all men and women. This is because not only are you eating less but, more importantly, your new anatomy itself affects the absorption of iron.
For the bypass, the part of the intestine that is bypassed is the area of the intestine that absorbs iron. Additionally, the amount of stomach acid is diminished in both the bypass and the sleeve, which reduces iron absorption with both procedures.
Thus, regardless of menstruation, you need iron supplementation just because of the operations themselves. In addition, women that menstruate may need extra iron on top of the recommendation after bariatric surgery.
As always, in order to ensure that your iron levels are where they need to be, get your blood tested at least once a year and follow your clinic’s recommendations.