Until version 5.21: No and because MongoDB is a different kind of database database I personally don't expect it soon.
As part of presales within Mendix we have been working on integration to Mongo DB. It is pretty straight forward as there are a set of Java libraries that you can use to integrate with MongoDB with. This will allow you to store certain data on a Mongo DB. This is currently just in prototype at the moment and would need some work to make it appstore ready.
If you want the Mendix database to run on a MongoDB, this isn't currently possible in 5.21.