No, Matt, the outcome would not have been the same, unless you're referring to Alfie's death. There was no reason not to return the child to his parents if he was so out of it and terminal, except a gay judge said no and it held on appeal.
I am glad you and David are happy with your healthcare system but I sure wouldn't want to be under it if I or somebody I knew had a rare and/or fatal disease - they ARE bureaucrats at NHS (the bureau) because they work for the government and are paid in tax dollars. But since they are bureaucrats, they're going to do everything by formula and try to apply their limited knowledge in cases like this one and Charlie's. Both of their conditions were so rare about nobody in the world "knew best", makes you wonder what they would have done with that Mask kid, Rocky or Steven Hawkin's parents if they weren't prominent in the British medical community. Already talked about a couple of cases here where the courts stepped in, realize that this is a complex and usually case by case situation, but you can see it can and does happen here. And so does the flipside:
What Does It Mean to Die? | The New Yorker
mother petitioned and won that case, still don't know for sure if she's alive or not but this is the other extreme.