No, since she's a "parentless 16 year old" this means she's in the foster care system -- thus, without a stable home or the ability to reliably provide safety and care for a newborn -- so, she will likely lose any parental rights pretty quick, even if she doesn't want to give the kid up.
There's an outside chance she could fight it and maintain stability until she's 18. If she has decent supports (case workers, a decent foster family), she might still not have had her parental rights terminated by the time she's 18, and able to legitimately argue that she can, as an independent adult, be responsible for a child. Of course, she'd likely be competing with a foster/adoptive family that has more resources, and will have had primary custody of the child up to that point.
That is if the baby appears healthy and without major disabilities from the start. Newborns/infants normally get adopted pretty quick, but those requiring extra care less so. Long and short, there's a decent chance this "parentless 16 year old's" child ends up lost in the same system that failed her.