Apparently, if you use Google Auth, your application can send from any email that has authorized your application. This means if you have any user authenticate with Google OAuth, you may send on their behalf.
However, sending from SendGrid or Amazon SES, may be easier.
With SendGrid may send from any sender without authenticating their address. SendGrid's "whitelabeling" (the $20 a month thing) is on a per domain basis and allows for DKIM & SPF signing of your messages, however this is not a requirement (as you can send without this). As a Google App Engine customer, you get 25,000 free emails a month, you may also use the SendGrid Lite Plan to send at $1 per 10,000.
Amazon SES does require sender authentication, although this is pretty simple to do. You can verify a domain or authenticate individual senders by sending them an email and having them click a link. Amazon will do DKIM and SPF signing for each domain you verify. With SES you may send to 2,000 emails a day on the AWS Free Usage Tier, with additional messages (or messages sent after free usage tier expires) costing $1 per 10,000
In the interest of full disclosure, I should mention, I'm a SendGrid employee.