I tried to test it, but I literally don't feel comfortable giving somebody full access to my email. I don't know your practices, security protocols, etc. I'd feel way more comfortable if this would be an app or a browser add-on that would handle everything locally, without sharing the access token with your servers.
The user logs into DarwinMail.app, DarwinMail makes a login request to Google's servers, Google logs the user in, DarwinMail asks for the users emails at which point this data is rendered in the user's browser. None of this email data is stored on DarwinMail's servers. There is no need! Think of all the space it would take up and the time that would be spent retrieving the data.
Google's API & servers do the heavy lifting. DarwinMail allows you to view your emails just like Inbox, and hopefully provides (or will soon provide) the same kind of functionality :)