MongoDB is dual-licensed with AGPL (the engine) and ASL 2.0 (the drivers). In a nutshell, merely using MongoDB through the drivers does not dictate to release your source code (due to drivers' ASL 2.0 license).
AFAIK, only if you directly call the mongo engine, you need to give out your code that's using it (but still not the application code that talks to mongo via the drivers).
Check this MongoDB blog entry: http://blog.mongodb.org/post/103832439/the-agpl
What if you deploy (install, configure) mongodb in your deployment scripts. And then start/stop/restart those processes. And then maybe create some users via mongo shell. Do you need to publish your deployment scripts?
(A bonus question: how can they publish the drivers as ASL 2.0 if those drivers use the AGPL-licensed part of MongoDB over the network? Because they are authors of both?)