It took me a while to figure out how to change the default from address in Outlook when using gmail or a google apps account. I've done it in Office 2010. This will make your alias the default email address when sending any emails. It won't say "on behalf of" or anything like that.
1. Set up gmail account in outlook if you haven't done so already
2. In file tab, open Options
3. Select Advanced Tab
6. Select your account and click Account Properties...
7. IMAP E-mail tab
8. Change E-mail Address: (not User Name)
Now when sending emails from the original account, the email address will actually be the new one even when the original account is selected.
Note: You can't use google apps sync with this solution; you have to use use calendar sync if you want use the calendar also.
If you just want to change the from address once, you can do this:
1. Create a new email
2. In options, select the from field
3. in the From tab, select "other email address" and put whatever address you want