Obviously yes, because it permits you to search your files. But not for Google Search (global), your data is private.
"Our systems scan and index emails and some other user data for multiple purposes; this scanning is 100% automated and cannot be turned off. Scanning enables us to, for example, perform spam and malware detection, sort email for features like Priority Inbox, and return fast and powerful search results when users search for information in their accounts. The scanning and indexing that our systems run also enable us to display contextually relevant advertising, including in Gmail. If your domain disables ads, we will not use your data to display such advertising to your users. Domains using the free Standard Edition of Google Apps cannot disable ads."
Does Google index Facebook pages?
Google index everything with unique content, You must follow Google guideline properly. Read this details post how to index Facebook or any other pages in google
If you are using duplicate content on your website then time to stop it because if you use duplicate content or contents from another web, then Google will punish you, You will not find your web in google search or google will take months to index your website.
Google always value real and useful content, so even if you copy any statement from any website then use that in blockquote. Google ignore that blockquote text, don’t forget to link to the source. Many webmasters think linking will ruin their website but its completely false. If you link to a useful source, then that will help search engine readers, which will increase your page value, because the users will not move back to the search engine from your website to look for what they are looking.
