You can easily embed MongoDB in your OEM solution but you need to consider 2 things:
The code is written in C++, so if you are implementing the code in a different language you might need to also have a wrapper that launchers the database process separately.
MongoDB is licensed under Gnu AGPL-3.0 which is a considered as a copy left server license. However, the MongoDb states that the intention of the license is to allow refinements to their code to be submitted back, and that your product will remain separate. This makes me think that the normal copy left rules don't apply.