Posted my response before I saw yours but correct, it works unless they wash out. Even with injuries, there are platoons they put them in until they heal. They also have "physical conditioning platoons" for those recruits who can't do the minimums of running, push ups, or whatever. Same applies. When they hit the minimums, they get assigned to a training platoon.
But people don't stay in the fat platoons indefinitely. They lose the weight and move on into training unless they get hurt and wash out.
Also, at least back in the day, once they're in training, they're on a restricted diet. (This also applies to recruits who are slightly overweight but not "fat.") They would have a red mark or something on their ID and at chow they'd only be able to eat things like lean chicken with no skin, veggies, no milk but juices. Shit like that.
I understand that boot camp is an extreme example but there were recruits whose parents didn't recognize them after graduation.