I really don't think Alice would have been sent on ahead - the job of a lady's maid was to be *near* her mistress so she could serve whenever she was needed.

Also, I don't think Eleanor was necessarily even worried about her father *opening* her letters. Things may have been different in JA's time, but from what I've read about English country houses in the early *20th* century, IIRC the mail was brought in and handed out while the hosts and their guests were at breakfast. If General Tilney saw a letter being handed to Eleanor and even *suspected* that it was from Catherine, I can imagine him making things unpleasant enough for her just for disobeying him! If Alice received a letter, she would at least receive it in the servants' quarters, away from General Tilney's eyes, and could hand it over discreetly later.