Hierarchical data in MongoDB?
The question to answer first is, are any of the possible children bounded or unbounded sets of data? The next question is, how are you going to be requesting the data? Another question would be, how often will the data be written? 

One of the things you'll learn quickly with MongoDB is the answer to any schema questions is almost always "It depends". It depends on the answers to the questions I asked above and a few more. To get you on your way though, MongoDB has some great documentation on the subject of hierarchies. This gets you part of the way to your solution.

Then you have to understand your data access patterns and when to normalize or denormalize data. Something to help you make that decision can be read in this great blog.

Sorry to leave you with a not so cut and dry answer. Yes, MongoDB can take care of hierarchical data. How should it be done? It depends. Will it be faster than MySQL, it depends. Can it be faster than MySQL? Most definitely. 

Scott