Ok, I just looked into it (even though I'm an Outlook expert about as much as I'm an opera singer).
1) Added my @gmail.com account in Outlook 2007.
- Surprise: automatic configuration chose POP3, which does not support access to server folders (Sent or otherwise).
- Fix: used manual configuration, chose IMAP as the account type, entered imap.gmail.com, SSL, port 993, and all the rest
2) Gmail's server side folders showed in Outlook, "special" folders were under [Gmail], as expected (Gmail uses [Gmail]/Sent, [Gmail]/Drafts, etc.)
3) Sent myself a test message from this account in AquaMail
4) The sent message showed in [Gmail]/Sent in Outlook a few seconds later
Based on the above, I can only conclude that the issue you're experiencing has to do with your Outlook configuration.
I'd say, check your Gmail account type in Outlook, and make sure it's IMAP. This is under Tools -> Accounts, it should be IMAP/SMTP and not POP/SMTP.