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It depends on where it is broke and how it heals. They can survive a broke leg but if it heals incorrectly, it could be devistating.
Let me share my personal experience with this (in a bantam at that):
I had a bantam that had it's leg broke on day one in the incubator. I cam back in to look in the incubator and saw this tiny bird stuck in the wire mesh. I opened the lid and gently picked up the weight of the bird (not getting it out yet... but looking to see why it was stuck) I saw it's toe stuck but it's "knee cap" was swollen and red. I immediately reconized that as broken and tried to get the wet chick out. I splinted the tiny leg... it would fall off. Splint it again, it would fall off again. The chick got around fairly decently, so I kept trying to splint it for the first two weeks (after that, it would already be healed and a splint is useless). It never did work right, but the chick still got around decently. I thought since it was a bantam, maybe it would just be a "special needs" chicken.
As time went, its size grew. That leg became even more a issue. One day it got it stuck inbetween the waterer and wall. It was there for at least 2 hours while I was out of the house. Eventually, I knew this was not going to work. (now here is the part in the story that I went from a hippy-type animal lover to a realist who cares and respects animals)
It's leg was starting to look more and more like it was turned almost backwards. The bird was (at a bantam) too heavy and it would hop, and sit... then hop, and sit. It's feathers stayed matted with poo because of it.
Finally, I took it outside, laid it in the grass. I let it eat and chip like it was happy to get out in the sun and get grass and (try) to get bugs. After a few minutes of this "free range" time... I had to shoot it.
That was BY FAR the hardest thing I ever had to do. Shooting a helpless chick out of it's misery is much easier. For one, it is easier to kill the bird at chick size, you aren't as attached to it either. This was a fully feathered bird who I was caring for and who I knew was suffering for this whole time. The guilt was far more.
Now, if your little pullet has a break in a place you can get a splint and keep it on... try. If it keeps failing... just save yourself and the bird from the future of suffering and hop and sit, and that inevitable day when you have to put down a fully feathered bird.
Good luck.