I have a django test suite that builds a DB from a 400 line fixture file. It runs unfortunately slow. Several seconds per test. 
I was on the train yesterday developing without internet access, with my wifi turned off, and I noticed my tests ran literally 10x faster without internet. And they are definitely running correctly. 
Everything is local, it all runs fine without an internet connection. The tests themselves do not hit any APIs or make any other connections, so it seems it must be something else.
This most likely means you've got some component installed which is trying to make network connections. Possibly something that does monitoring or statistics gathering?
The simplest way to figure out what's going on is to use tcpdump to capture your network traffic and see what's going on. To do that:

Run tcpdump -i any (or tcpdump -i en1 if you're on a mac; the airport is usually en1, but you can double check with ifconfig)
Watch the traffic to get some idea what's normal
Run your test suite
Watch the traffic printed by tcpdump to see if anything obviously jumps out at you
Django Tests run faster with no internet connection