It depends entirely on how "Django-like" you need your models to be.
If you're expecting to be able to just drop a MongoDB store into your project and have any arbitrary Django app run with it -- that's going to cause problems. There are fundamental differences between SQL databases and MongoDB, and it's not possible to abstract away those differences. In particular, deep joins are very difficult/inefficient to implement on Mongo, because Mongo hasn't been optimised for that lookup mode.
However, if you're just looking to be able to do some light introspection -- say, enough to use ModelForms, and maybe some light local attribute querying -- then you should be able to duck type the Django model Meta object and the model manager sufficiently to make simple operations work. I'm not aware of anyone that has tried to do this, however, and the Meta object in particular isn't currently a documented interface, so you're going to need to get to know Django's internals in order to take this approach.
Is there anything you can use out of the box? You might get some traction using django-nonrel, but I can't comment on how well it works. It's a fork of Django 1.3 IIRC, so it's getting quite old in terms of feature set.
There's also an old GSoC branch that introduced a MongoDB backend; however, that effort stalled due to some complications with automated primary keys and a few other areas. You might be able to resurrect some code from this branch, but again -- it's somewhat stale, and not especially well documented.
Yours,
Russ Magee %-)