As far as I can see, there isn't any PDO wrapper for MongoDB, and there isn't any code that allows to use MongoDB as database for Drupal, simply for the fact Drupal expects to use an SQL database engine, while MongoDB is not an SQL database. You cannot generally convert a static query into code that uses MongoDB.
The Mongodb module allows you to use MongoDB in those cases where Drupal is not expecting to get data from a database, although the default implementation uses database table. That is what happens for the cache, entity fields, and Drupal queue, for which a module can define a new PHP class to implement a different mechanism to store data.
Notice that the Mongodb module is not tightly integrated with Drupal entities, as it doesn't use any Drupal entity to work. It eventually allows you to store field data in Mongodb, but that is an additional module you can eventually use. If you are not interested to store field data in MongoDB, the main module (mongodb.module) still works, and can be used from the other sub-modules.