Facebook and DropBox have an approval process that must be followed before to release an app, otherwise the app are going to have some limitations (e.g. a maximum number of users or access to a restrict set of permissions for the user data).
Is there a similar process in the Drive?
As @DalmTo mentioned, Google Drive uses quota limitations.
By default, your app gets a 10M Queries/day quota limit. There is currently no restriction on Auth scopes allowed or number of users. Obviously though, as the number of users grow, that 10M query cap may become more of an issue. E.g, once you hit 1M users, that's only 10 queries per user per day. (Drive's last announced Active users was 240M).
To increase your quota, we request that you fill out a form with some basic information. Based on the nature and size of your integration, we may ask to do an architectural review with you.
The main purpose of this is to ensure that larger integrations behave well under error conditions (See Handling API Errors), as well as using the API as efficiently as possible.
We don't charge for increased quota with the Google Drive API.
During reviews, we may ask you about auth scope usage. While we don't restrict which scopes your integration can use prior to any reviews, it is in your's and your users' best interests to use the most restrictive scope that will get the job done. In most cases, this is the drive.file scope.