When I select heat at the thermostat on my goodman furnace and the pilot light is out is the circulating fan supposed to come on/

No, the fan shouldn't come on until after the burner is going, See sequesnnce of operations of a gas furnace, https://www.askmehelpdesk.com/heatin...ons-58313.html

The fan should come on in the fan on position, but it uses a different motor winding and relay as heat.