They usually check out the ovaries during the section, I know b/c it's noted on the operative reports. I don't know when they do this (I'm usually helping with breastfeeding in the OR at that point, rather than watching the surgery). I suspect it's after the uterus is replaced. Not all surgeons here are doing the "deliver the uterus" style of section, it depends on when/where they trained.
I think fallopean tubes are so insignificant, comparatively, as to be unnoticeable during the section. What we need is a surgical RN or OB/GYN to tell us.