Probably no. Burnt rice will smell burnt and turn black and impact a lot of the rice.
I've burn rice, and it ends by discarding everything.
On the other hand,
There is a brief moment between cooked rice and burnt rice when the rice on the bottom of the pan is just getting crispy, like the Paella's socarrat.
The simple explanation is firewood produces smoke and other sources of heat don't. Smoke imparts aroma and flavor to the dish. Firewood doesn't cook the rice any better than a gas or induction range or a rice cooker, it's just about the smoke.