Hicks and Newt had to die in the beginning of Alien 3 in order for the film to thematically even be an Alien film.
At their heart, the films are about Ripley being alone, more in common with the titular alien than with her termporary allies. She's an outsider in her crew. She's a civilian among marines. She's a woman among convicts. She's lost her child, she's lost 57 years of her life. The Alien is her only real touchstone now, and in a way that is very expressly shown in the films, that becomes a kind of "relationship" in itself. She's closer to the alien than she is to the people who surround her.
If Hicks and Newt survived and were part of Alien 3, it takes that away and makes it an ensemble cast, which thematically doesn't fit, and (I think) it's one of the reasons that a lot of the new Alien films just don't feel like Alien films; they're missing that key thematic ingredient. Ripley is a tragic character, doomed to battle alone against the only thing she has left in her life.
The Xenomorph has been the only constant in her life throughout the entire franchise. Everyone else is temporary. So basically...yes...in so much as a nemesis can be a situationship.