Congratulations on your first posts, Nikolai.
It does indeed depend on the content of the letter.
Amalia is what? 16? Most letters won't reach her, I'd say.
Obviously letters that are remotely rude or contain extreme political, religious opinions won't reach her.
Love letters and letters that are over-the-top admiring won't either. Or letters that contain too personal details about the writer. At worst they'll end up in the "potential stalker" pile.
Letters containing requests, pleas are also unlikely to reach her, unless they somehow involve something she is involved in - and considering that she has no official role yet, well...
To be short: If her mother shouldn't read a letter to Amalia, chances are that the staff decides that Amalia shouldn't read it either.
A friendly, polite letter or a latter congratulating her on something is IMO the most likely to actually be read by Amalia. - If se has the time.
So if I were you, I would not expect more than a polite standard reply.