You can only skip the counter if you go online, via
Alamo's website, and add in the driver's information (DL #, expiry date, etc.) and payment details. That will generate a pick up pass with a barcode that they can scan at the gate. You can go straight to the garage with that pick up pass, choose your vehicle, then drive to the gate with the pass, your license, and your credit card all in hand to show the agent.
We have been able to skip the counter even with our 3rd party reservations through Costco. In addition to the Costco reservation number, we are assigned an Alamo reservation number. You can put that Alamo reservation number in on their website and do a "look up" of your reservation, which will allow you to follow the steps to first "check in", and then "skip the counter". So as long as
UT gives you the Alamo reservation number (not just a UT reservation number) then yes, you should be able to skip the counter and go straight to the garage so long as you complete the check in and skip the counter steps online in advance of your arrival.
