They can depending on how you raise them.
My girls belonged to a friend first, who kept them in a large stall with food 24/7. They were fat unhappy girls who never got exercise, but laid eggs well.
When said friend moved the girls were about 1-ish and came to my farm where they got to be outside, in the sun, and had a small hill to traverse. There were bugs to eat, dust to roll in, and other chickens and turkeys to mingle with. Food was more restricted and they had to move a little bit when they were hungry.
After about a month they had lost a few pounds and became rather active for their size. One had ongoing eye problems, lids misshapen-probably genetic, but other than that I'd say they did quite well.
I doubt a BBW tom would have lasted very long though. And they certainly wouldn't be able to breed very well. The BR tom didn't have a problem...they were like tables compared to the BR hens. Really big tables!
That used to be my tom turkey. Best. Watch. Dog. Ever.