Yuzu wouldn't push for Izzy to join her. Heck, she's already pretty bashful about being up there already by herself (she's just here because she did end up singing when she was in Celliwig the first time around and so her confidence in her voice is a little bit higher). Still, she'd feel very thrilled to know that her girlfriend is there and cheering for her! It'd even help stave off some of the nervousness.