Yes, but it won't resemble the way we do it.

The mechanism by which an organism will produce graphene won't resemble any of our crude chemical processes. Living things use proteins called enzymes to perform all of their chemical reactions. Enzymes are incredible molecular machines that facilitate nearly every biochemical reaction. There's no reason to think an enzymatic process couldn't produce graphene, or indeed, that there might not exist an enzyme or pathway of enzymes that make graphene already that we simply haven’t discovered. But, importantly, that enzymatic process isn’t going to resemble any of our existing methods.

An example of this would be the production of ammonia in biological and artificial processes. Most industrial ammonia today is produced by the Haber process which relies on extreme pressure and temperature to catalyze the reaction of nitrogen gas to ammonia. Meanwhile, in the soil around us, tiny bacteria produce enzymes called nitrogenases that make ammonia from the same nitrogen gas without the need for high pressure or temperature. Evolution is much better at organic chemistry then we are. There likely could or does exist a biological alternative to the Tang Lau Method for the production of graphene that doesn’t require high temperatures at all.

Yes, but it won't resemble the way we do it.

The mechanism by which an organism will produce graphene won't resemble any of our crude chemical processes. Living things use proteins called enzymes to perform all of their chemical reactions. Enzymes are incredible molecular machines that facilitate nearly every biochemical reaction. There's no reason to think an enzymatic process couldn't produce graphene, or indeed, that there might not exist an enzyme or pathway of enzymes that make graphene already that we simply haven’t discovered. But, importantly, that enzymatic process isn’t going to resemble any of our existing methods.

An example of this would be the production of ammonia in biological and artificial processes. Most industrial ammonia today is produced by the Haber process which relies on extreme pressure and temperature to catalyze the reaction of nitrogen gas to ammonia. Meanwhile, in the soil around us, tiny bacteria produce enzymes called nitrogenases that make ammonia from the same nitrogen gas without the need for high pressure or temperature. Life is much better at organic chemistry then we are (it invented it after all). There likely could or does exist a biological alternative to the Tang Lau Method for the production of graphene that doesn’t require high temperatures at all.