Will nolvadex (tamoxifen) in women affect their birth control?

YES. Nolvadex (tamoxifen) is used for breast cancer patients it is antiestrogen type drug it will affect ovulation it will not be advisable to get pregnant because of potential carcinogenic effect.
Not recommended. Hormone containing birth control is not recommended with novadex as it counteracts its method of preventing/treating breast cancer. We recommend non hormonal methods like iud's, foam, condoms, or sterilzation.