Looking at the full headers for two emails sent to me, it's easy to notice the difference with emails sent from Gmail using Mail Fetcher, and emails sent using Google Apps for your domain.

The first screenshot is what you want to occur, if you're using Gmail for your domain. There is no indication that Gmail is handling the sender's email.

In the second screenshot, which uses standard Mail Fetcher, you'll notice the Sender field, which displays the Gmail address used to maintain the external email account. This is what you don't want, because some email clients (specifically Outlook) will show your incoming mail as:

real_email_address@mysite.com

on behalf of

gmail_address@gmail.com

This is poor branding, especially when your real email address is for your company, but you manage it in Gmail.

So I'd recommend using Google Apps for your domain whenever you'd like a complete branding experience for external email accounts. Mail Fetcher is handy, but not always the best choice since it doesn't completely hide your background management system.