I would find the idea of being given a shirt I can actually wear so appealing I'd be tempted to change into it right there at the booth.
And no, I don't wear men's shirts, and no, men's shirts are not gender neutral. Men's shirts always squeeze the boobs uncomfortably, while bagging loosely and unflatteringly around the waist.
I work in an industry where the crew often gets a T-shirt at the end of the project, and the one time I actually got a woman's shirt I was so happy I wanted to cry.
What's important to me here isn't the idea of getting some swag T-shirt, but feeling included and cared about by an industry that often forgets we exist. Hooray for Rockstar!