No.
Disconnect the relays one at a time and just turn the ignition to on. There should be no need to start the engine.
You should also check the temperature switch's connector to see if it is connected. If the computer can't read the switch (i.e. if it's disconnected), the computer runs the fans all the time as a safety measure.
TEMPERATURE SWITCH is:
UNDER HOOD, PASSENGER SIDE, UPPER ENGINE AREA, NEXT TO DISTRIBUTOR, MOUNTED IN PASSENGER SIDE OF WATER OUTLET