Is NaHCO₃ a carbonate?
Carbonates are salts and esters of carbonic acid $\ce{H2CO3}$. 

In generic nomenclature you may therefore consider a hydrogen carbonate also a subset of all carbonates. They are sometimes also referred to as primary carbonates.

Another considerable point is, that the structural subunit $\ce{O=C(-O-)2}$is still conserved.

In a stricter sense a hydrogencarbonate is only all forms involving $\ce{HCO3-}$, so it appears to be not a generic carbonate, but a class of its own. This refers to its one $\ce{O-H }$ bond and therefore it being a different structure.

However, another point of view should always consider aqueous solution equilibrium.
\begin{aligned}
\ce{HCO3- + H2O &amp;&lt;=&gt; H3+O + \color{\red}{CO3^{2-}}}\\
\ce{HCO3- + H2O &amp;&lt;=&gt; H2CO3 + {}^{-}OH}
\end{aligned} 

You can see that carbonate ions will be present to a certain extend in solution. The chemistry will therefore also to some extend resemble the chemistry of the carbonate.

Chemical properties of bicarbonate compound might differ from the pure carbonates - incorporation of water, solubility, ... .

On another page, in organic chemistry the compound class carbonates refers to structures of the type $\ce{\color{\red}{R}-{CO3}-\color{\navy}{R'}}$, where $\ce{\color{\red}{R},\color{\navy}{R'}$\in$ Alkyl, Aryl}$ - hence esters.

To sum it all up, since a more stringent definition of carbonate is not present to me, I would always consider a bicarbonate a carbonate.