I mean, it would technically be possible to build a computer out or organic and biological live tissue. It wouldn’t be very practical but it’s technically possible.
I just don’t think it would be very reasonable to consider that the one thing making it intelligent is that they are made of proteins and living cells instead of silicates and diodes. I’d argue that such a claim would, on itself, be a strong claim too.
Even if they did hallucinate answers, it wouldn’t be the first game that relies on the “unreliable narrator” trope.