Not really, bones are usually not circular / rectangular in cross-section, which is assumed by this relation. It’s also not necessary if you have the CT images because BoneJ calculates section modulus (Zmax and Zmin), without need for assuming annular geometry.
That seems likely. Bear in mind that that the chord length that you divide I by to get Z is measured as the perpendicular distance from the principal axis to the most distant point from the principal axis. This is because this point is the one that will experience greatest strain under an applied bending moment, and so is where failure is most likely to occur. If you have included something in your ROI, as small as a single pixel of noise, that is a long way from the principal axis in comparison to the perimeter of your bone, you will get wrong results for Z.