After having surgery from removing a ovary, do u really have to wait 6 weeks to have intercourse?

Let it heal. I would follow your doctors instructions. Inside your body there are dissolvable stitches or cauterized areas that need to heal. Intercourse can be traumatic to these fragile tissue areas. Avoid vaginal penetration but other external sexual activities should be fine.
Yes, please do. There are a number of reasons doctors prescribe six weeks of pelvic rest (no intercourse, tampons, etc). Pelvic rest allows your body to heal from the incisions you received, without any added risk of infection from outside sources (including your partner). Your doctor is not exaggerating when he or she says six weeks, either; it's the shortest time recommended to heal from gynecological surgery.