I think you've written a very compassionate letter. I think it shows appropriate concern, without threats or an ultimatum. It shows respect and encouragement. It sounds honesty and is not demanding.
I think it's a very appopriate way to reach out to someone you love that has this problem.
I'm sure you're aware that it might not help, that sometimes our A's are beyond reach, that they need to be the one to ask for help and this might not be her time, but I think a letter sent like this could be very helpful.