Yes, you can keep them but you have to care for them differently and don't expect them to live as long as a heritage turkey.
You should ration their feed, to slow their growth so that their mass doesn't out pace their bone growth. Unlike cornish cross chickens which get their freakish growth from a final genetic cross that is meant to be deadly, broad breasted turkeys are actually breed through A.I., with the adult flock being kept on a calorie controlled diet to give them longevity.
I would think feeding your white a lower protein diet, with lots of grains and greens should help. It wouldn't hurt to give her some vitamins in her water, to balance out any that may be missing from her feed. I know that hinkjc had a female that was at least three years old last summer. I remember her mentioning that she was a sweet bird that moved pretty slow but I don't remember if she ever got any fertile eggs from her.
I have had them make it to past a year and my bb bronze last year was laying, she even had a fertile egg develop by accident in a duck nest... What eventually got her was a hip injury caused by a pair of rowdy tom slates, so I have no idea how long she could have lived.
