Tubal ligation doesn't have an impact on ovulation or menstruation. It simply prevents the passage of an egg into the fallopian tubes thus preventing fertilisation and implantation. Unfortunately it is unlikely to help with your ovarian cysts. Most OB's won't do this procedure during a c-section due to an increased failure rate.

The OCP can help with the ovarian cysts through inhibiting ovulation if that is a possibility for you - although maybe not a long term option. Good luck.