She is very likely to survive. But managing with only one leg, I'm not sure about. How much of the leg is left? Half? One quarter? More? Less?
The biggest problem you are going to have after the leg heals, may be poop getting on her rear-end for the rest of her life. She MAY learn to get up on the one leg and just hop around. But if she doesn't learn or try that, you'll have to clean her rear end quite often since she can't stand up away from the ground it will fall on.
Chances are, she'll still TRY to move around, and she'll still find ways to flap her wings for exercise. She'll definitely become your closest pet, and be happy sitting in your lap a lot (it's going to be one of the few places she'll feel safe). But whether or not she'll be able to leave one particular spot is the question, and it depends on how much of the leg remains, and how willing she is to try anyway.
Also, if she doesn't learn to "hop" around, once she gets older, be prepared to physically take her outside and set her in a grassy spot to find bugs and/or eat grass blades. You'll have to sit with her while she does so she doesn't feel like she's in danger and abandoned. And feel free to take some meal worms or crickets, and seeds out to toss in the grass for her to "find".
One more thing.... that fox WILL return. He just found a source of food, and he knows there is more left. Keep them locked up tight, and ask around about getting a local trapping service to come remove him. The fox I have a problem with never took "a leg". He took entire full-grown large-fowl rock hens at once, and I wouldn't find any piece of them remaining except feathers.
