On the plus side, she wrote 'Welcome to the AAA Club!' in lipstick on the bathroom mirror, and left me a membership/roadside assistance card on the counter.
This comic is a reference to an old urban legend: a guy is drugged (often after being approached by a flirtatious woman), then he awakes in an ice-filled bathtub only to discover that either one or both of his kidneys have been harvested by organ thieves.
In this comic the situation is reversed: Beret Guy is bringing ice to a party, when he's lured by Danish up to "her place" and drugged. The next morning he awakes in a bathtub filled with kidneys, realizing that his ice has been stolen.
The title text refers to a similar story where the victim is left a note by their captor or one-night stand that says "Welcome to the AIDS club". Rather than having been involuntarily infected with HIV/AIDS, the victim, Beret Guy, has been involuntarily enrolled in the American Automobile Association (AAA) and his roadside assistance card has been left on the counter. This could also be another pun on Beret Guy's response of yelling AAAAAAA, which could be another kind of AAA club that he is welcomed to.
There is no display of typical "Beret Guy behavior" in this comic, although it is typical for him to be involved in an incident that turns the world upside down. His encounter with organ thieves only cost him his ice, a party and that he got a nasty experience. But he retained his kidneys and was not infected with HIV (probably).