No they don't. This is the reason why this is such a hell. Yes, the account acknowledges the alternate name, but Google keeps publicly replacing it with the primary name as soon as you do anything.
This is not just ugly and confusing from a marketing and branding perspective, it leads to all kinds of complications with software that reacts to email-addresses, or services that are coupled to Google Apps.
Perhaps I am not following 100%, but I believe we have done this without this issue for years with google apps.
We have one primary domain and 15 alias domains.
Email Example: user@alias.com gets an email, when they reply it stays set to the alias, it doesn't change to the primary domain.
Gmail sends a Sender: header with the account's primary email address, which some email programs treat as the "actual" sender. Some mail programs display this as "From alias@example.com on behalf of primay@example.net" and then those programs use the primary as the return address.
According to Google, they don't include this header if you upgrade to Google Apps for Business.
This is not just ugly and confusing from a marketing and branding perspective, it leads to all kinds of complications with software that reacts to email-addresses, or services that are coupled to Google Apps.