Hi Blackie,
No, please don't remove the relay from the socket. It is required to successfully run this test. Remember that the temperature "relay" is not a relay; it is a complex electronic module. When you ground the "E" input, you are simulating the conditions that would be present if the engine was overheating. The temperature module will sense this low resistance and turn on the fan. If the temperature module were missing, nothing would happen if you tried the test.
In all cases, the temperature module must be present for the diagnosis to work.