Today if you want to file email from Gmail to Content Manager you need to use the Email Link module. The limitation of this is that there is not user interface so you are unable to fill in the Record data entry form.
Gmail supports add-ons making it theoretically possible to create a client side solution which will allow the user to complete the data entry form at the time they file the email. These add-ons are constrained in that they have to be able to function both in the Gmail web UI and also the mobile Gmail app.
Exploring the possibilities
The sample in this video demonstrates the possibilities and the limitations of a Gmail add-on.
Given the current limitations of the UI components it is difficult to see how we could build a generic add-on. Any customer or partner who wants to build a custom add-on is welcome to start with this sample, as always feel free to contact me if you either have suggestions for an 'off the shelf' Content Manager add-on or want to discuss the building of a bespoke solution.