No and Yes
With proper selection and an experienced surgeon - the survival rate is the same for lumpectomy
(+ radiation) and a mastectomy
But even in the best hands, about 5-10% of women will have a recurrence in their breast after lumpectomy and radiation. (more common with larger tumors, younger women, and positive lymph nodes). Most of those women can be potentailly cured with mastectomy.