No you will not have anymore periods.
I opted to keep my ovaries against my doctor's wishes. I just didn't want to surgically go into menopause. I wanted it to happen natuarally. I almost didn't have my cervix taken too, but the doctor talked me into it because he said that since the cervix is attached to the uterus, that there could be a chance of fibroids reforming since some of the uterus might remain and I could also experience some bleeding. Atfer all the bleeding I had due to the fibroids before surgery, I just could not go through that again. Fortunately I do not have any history of ovarian cancer, but I will have to continue yearly pap smears.
I wonder why your Dr did'nt do a complete hysterectomy? I would ask him why he left your ovaries.