Answer
True.
Work Step by Step
Since curl is simply chain rule with the partial, and that $\frac{\partial R}{\partial x} +\frac{\partial Q}{\partial x} = \frac{\partial(R+Q)}{\partial x}$, it follows that curl$(\mathbf{F}+\mathbf{G})=$ curl $\mathbf{F}$ + curl $\mathbf{G}$.
