Django session race condition?
Yes, it is possible for a request to start before another has finished. You can check this by printing something at the start and end of a view and launch a bunch of request at the same time.
Indeed the session is loaded before the view and saved after the view. You can reload the session using request.session = engine.SessionStore(session_key) and save it using request.session.save().

Reloading the session however does discard any data added to the session before that (in the view or before it). Saving before reloading would destroy the point of loading late. A better way would be to save the files to the database as a new model.
The essence of the answer is in the discussion of Thomas' answer, which was incomplete so I've posted the complete answer.
Summary: is there a race condition in Django sessions, and how do I prevent it?
I have an interesting problem with Django sessions which I think involves a race condition due to simultaneous requests by the same user.
It has occured in a script for uploading several files at the same time, being tested on localhost. I think this makes simultaneous requests from the same user quite likely (low response times due to localhost, long requests due to file uploads). It's still possible for normal requests outside localhost though, just less likely.
I am sending several (file post) requests that I think do this:

Django automatically retrieves the user's session*
Unrelated code that takes some time
Get request.session['files'] (a dictionary)
Append data about the current file to the dictionary
Store the dictionary in request.session['files'] again
Check that it has indeed been stored
More unrelated code that takes time
Django automatically stores the user's session

Here the check at 6. will indicate that the information has indeed been stored in the session. However, future requests indicate that sometimes it has, sometimes it has not.
What I think is happening is that two of these requests (A and B) happen simultaneously. Request A retrieves request.session['files'] first, then B does the same, changes it and stores it. When A finally finishes, it overwrites the session changes by B.
Two questions:

Is this indeed what is happening? Is the django development server multithreaded? On Google I'm finding pages about making it multithreaded, suggesting that by default it is not? Otherwise, what could be the problem?
If this race condition is the problem, what would be the best way to solve it? It's an inconvenience but not a security concern, so I'd already be happy if the chance can be decreased significantly.

Retrieving the session data right before the changes and saving it right after should decrease the chance significantly I think. However I have not found a way to do this for the request.session, only working around it using django.contrib.sessions.backends.db.SessionStore. However I figure that if I change it that way, Django will just overwrite it with request.session at the end of the request. 
So I need a request.session.reload() and request.session.commit(), basically.