Where does this "On Behalf of:" text appear? I just tested this, and sending an "on behalf of" email to another gmail account doesn't result in this text appearing anywhere in the gmail client. The original mail address appears in the headers under "Sender:" with the alias mail address appearing under "From:". However, if you open the email in gmail and don't check the headers manually, there's no indication it's not from the alias address. Replying to such an email, the "To:" field populates properly with the alias address.
In gmail, you'll be able to see the person's "secret" main email address in the `Sender:` field after clicking `Show Original`.
The real annoyance is Outlook. If someone responds to that email via Outlook/Exchange, the reply will be sent `To:` your main email address rather than to the address you sent with.
