If they are good friends then yes she will be in mourning because she most likely knew her (there's also a bug going around that Sims will grieve a sim they barely know.) but a good friend means high relationship so yes she will mourn. They said grief will act like rl so it will take time to heal.
I had a new Sim that missed out on the 'Welcome Wagon' and is now mourning someone I don't think they ever met - and I mean mourning them hard. Suffering sadness, getting various 'grief' related moodlets almost every day. Finally got so irritated I deleted them.
That's the bug they not suppose to mourn a person they barely know report that bug you're probably not the only one.
