Yes, as a new Gold member, you do not have to go to the counter for your first rental when renting at an Ultimate Choice location. With the introduction of Ultimate Choice, this is no longer a requirement, yet it continues to come up regularly in the forums from new members. Anything that needs to be done can be done at the exit booth.
Assuming that you booked anything besides an economy car, compact car, or manager's choice, just grab a vehicle that corresponds to your Gold level (Gold, 5 Star, President's Circle) and then drive to the exit booth. They will check your license and scan your credit card there and you should be good-to-go. We have given this advice to many people and not a single one has had an issue.
Safe travels!