Mary Ann, we just did this in Denver three weeks ago. If you've checked in online and set up your prepaid situation ahead of time, Alamo has you print a scannable page with a barcode on it. The directions on this page indicate that after collecting your luggage in Denver, you go to Island 4 (I think it was) to board the shuttle bus to the rental car center. When you get off the shuttle, skip the counter and head right to the Alamo parking area. You locate the size car you reserved, choose the car you want, load up, and drive to the exit. You present the scannable document to the gate agent, along with your ID, they scan it, and you're on your way. Took only a few minutes. It was all actually easier to do than it was to type this about doing it.
The caveat: We reserved an Intermediate car via the Costco website. Alamo at Denver calls that "Mid-Size." So the signage was different. Once we confirmed with an Alamo worker that Mid-Size is what we were looking for, there was only one vehicle there. Nothing to choose from, unless we wanted to wait for another car to be delivered from the clean-up area. The car in question was a Chevy Cruze, which was a perfect choice, but I was a bit cautious since there weren't any others to choose from. Granted, it was late morning on a Saturday. The car looked fine, and worked out very, very well over the fourteen days and 2400 miles we put on it. I'd rent one again in a heartbeat. Excellent option, for a rental car.
Dave