Have to chuckle.
Spur the Unicorn has appeared next to my Sim's barn three times. Each time my Sim told him to "Stop Doing That," and then shood him away. Still, he's listed as a BFF on my Sim's Relationships panel and he sent her a wedding gift when she was married. Maybe, if we could have more than six pets I might invite him into my household, but as is I have no room for him. Nevertheless, this goes to prove you don't have to make any special effort to adopt them.