You can take any car on the EA if you have an EA reservation with intermediate or full size. But there's no guarantee that there will be anything bigger than an intermediate. That's why it's a good idea to make the reservation as full size, that way you can go to the full size aisle and pick there instead if there's nothing on the EA you like. If you book intermediate, you can only go to the intermediate aisle if there's nothing you like on the EA. Full Size usually comes up the same price as intermediate when you book through Emerald Club. Your reservation will say full size OR your choice from the Emerald Aisle.
I've never spent more than 10 or 15 minutes from entering the garage, picking a car, checking out and on the road to WDW. There's usually one that catches my eye, I glance around for anything better and then we load the luggage. There's usually no more than 2 cars ahead of us at the checkout.