I'm pretty sure she would know how to do sign language because it would be faster to talk to people that way than to write it on paper. Especially with her family.
I have a friend with aphonia and I'm pretty sure she never bothered learning any sign language at all. She mostly just writes on a little notepad instead. Although perhaps it's likely she's an outlier and most people with the same or a similar condition would at least learn the basics.
I also suffer from selective mutism but in my case it's not nearly severe enough that I would need to learn to sign.