Multi threaded webserver vs single threaded
Having several threads or processes will indeed help you (indeed it's in practice required) when you want to handle more than one request at a time.
That doesn't mean that the two requests will be handled faster. Having a pool of processes or threads is very helpful for webserver performance, but that's not really noticeable in cases like this (unless you have multiple cores). But MySQL has no problem handling two requests at the same time, so if your webserver can do it as well, then you get rid of the problem of handling just one request.
But if it's worth the effort to start using such a server only you can answer. :) Django is surely overkill in any case, look at some small WSGI server.
We have a simple webserver for internal use that has only one duty: listen for requests, read them, and push the data in a database. The db and webserver are both located on the same machine. The db is a mysql-db and the server is a python webserver (BaseHTTPServer.HTTPServer) which runs single threaded. 
The problem is that two requests can't be handled at the same time. The question is, would it help to make the webserver multi-threaded (using django, cheryypy,..)? Intuitively, the webserver is only performing CPU consuming tasks so changing it to multi-threaded shouldn't help. Is this correct?