However, for me to claim that quantum Gravity is only emergent without a particle like graviton's mediation, I would need to present evidence. Just like this claim - quantum gravity is only possible from gravitons.
Now, as to how plausible this is, we'll actually get into semantics. To me, saying that "gravity is quantum" would mean that it is a real force/interaction, and that this force obeys the Heisenberg uncertainty principle. So, I wouldn't say "gravity is quantum" if it turns out that the Entropic gravity theory is true, as in that theory gravity is only an apparent interaction. However, I admit that this may only be my perception of what these terms mean together, and that others may use "gravity is quantum" to refer to any theory that explains the macroscopic effects we call gravity in a way that matches quantum theories.
If I am understanding your counterpoint correctly, then this argument can only be concluded satisfactorily if either Graviton is observed (proving is existence) or something more fundamental and deeper is observed (proving that quantum gravity can emerge without graviton).