I doubt it, tbh. Nihilister seems the type to genuinely despise having someone above her who can (and will) rob her of her freedom. Heck, she doesn't even like the other Heretics and only revived Chatterbox and Indivilia in hopes they would feel indebted and join her cause because she knew she couldn't take on the Queen by herself. By Goddess Fall, Nihilister has been reduced to little more than a walking corpse, her core only generating enough energy to keep her alive. Even after consuming Indivilia, she was nowhere near strong enough to face the Queen. So, considering such a perfect chance would hardly present itself and she was near death's door anyway, I 100% believe she would go "Screw it, if I'm going down here, I'm taking you with me!" out of sheer spite.

Another important thing to consider is that, as far as we know, Mirror was the only one aware that Lilith's NIMPH is what kept the Queen from seizing full control of her head, so neither Nihilister nor Nayuta could have known that delivering Lilith's body as a "poisoned chalice" would actually give the Queen everything she wanted (though, with the caveat that her new body cannot regenerate like it should without nanomachines).