Quick–how many of your tests would fail if you were not connected to a network (for database, files, services, etc)? How many of these are labeled as “unit tests”?

Do you have a way of quickly determining which tests are dependent upon that network connection? Can you easily run all the tests that aren’t dependent upon the network? Do you find that there are errors/failures in surprising areas?

Try it and see. You may learn something interesting about your code’s dependencies.