Is this a good story idea?

Yes, I think it works. Freedom comes in many forms, not just the most obvious. Your idea is original and likely to be unique among the stories submitted in your cl. That's a real plus in and of itself. You just need to be mindful of the "freedom" theme when you write it. Try to make as many ogies as possible between the bird trapped in the cage and the person trapped (by the coma) in his or her mind and body. You might want to employ terms like "frozen" and "locked in" to describe the patient. As you've already suggested, the "freedom" comes when the patient awakens from the coma. It definitely works. It *is* original. And I like it.