Yes, this is true. Since there exists a 'decoder' $Q$ which gives a value (close to) $\frac{1}{2}$, the pair $(A,Q)$ are $(\ell_2, \ell_1)$-instance optimal (see [this talk][1] of Foucart for details).


  [1]: https://www.math.tamu.edu/~foucart/seminar/Lect4.pdf