Let me see if I understand properly...
You want to impress a girl/travel enthusiast by taking her to the Austin airport concourse and UC? I'm not going to judge, but I'm sure there are more interesting aviation dates to dream up. I mean, it's not like you're going to watch Concorde take off. To me personally, the shorter the airport experience, the better. Are you sure this girl is going to be impressed with this idea? Or could it backfire cringingly?
Also, and I don't mean to defend UA's terms at all, but it would be pretty obvious to anyone looking that buying two fully-refundable tickets that are then, miraculously, refunded the same day, does not fit into your typical buying pattern (which, if you are a 1K, must be a bit).