Now Google searches Gmail Conversation in Google.com
From Today, Google is experimenting in basic Search Results. When you search on Google, It will show relevant Emails from your Gmail account along with basic Search Results.
Search Page will look like as below.
Currently, this functionality is on trial but registration has started for early access. You can join this trial at https://www.google.com/experimental/gmailfieldtrial.
Most visited Search Engine Google always experiments new features with few users for trial.