Yes, if the key is on, fan switch is on, AC button is in, fan should be running. Some folks have mentioned a nonmoving fan with those conditions will start running when you push the blades with your fingers; if so, that is a bad fan.
Plus, the 384 relay can become intermittent because of a faulty solder joint. Take off the side panel on the dash you see when you open the door. You can then see the # 384, and pull it off with fingers. Take the cover off and look at the solder joints closely. There is one that is susceptible to a crack. It can be fixed, and it can be good to have a spare, if you like. Good luck!