Chapter 3 - Motion in Two Dimensions - Learning Path Questions and Exercises - Conceptual Questions - Page 95: 8

Yes, $\vec A+\vec B$ can equal zero.

For non-zero magnitude vectors $\vec A$ and $\vec B$, $\vec A+\vec B=0$, for all $\vec A=-\vec B$. That is, when $\vec A$ and $\vec B$ have the same magnitude and are pointing in opposite directions.