sodium hydrogen carbonate is a carbonate and a base, so if acid
is added to it, will it react with its carbonate property or its basic property? 

Sodium hydrogen carbonate (NaHCO₃) is a base and when an acid reacts with it, it forms a base and carbon dioxide is released.
For example:
NaHCO₃ + HCl $\to$NaCl + H₂O + CO₂