If it's truly 100% derived from wood,yes but sawdust,wood chips,small twigs and other wood will do the same. Just don't use Walnut,Cedar,Cypress,Osage Orange.

Paper and cardboard are also good sources of carbon.

thank you. good point. I am not sure if they all natural but they are very generic ones .

Raw/natural charcoal is fine but BBQ briquettes often include petroleum products or have been treated with a petroleum substance that helps them catch and burn faster. These you want to avoid.

Unused charcoal would be bad idea. Thanks for clarification.