Converse overtwistedness conjecture for the ECH invariant f

Let $(Y,\xi)$ be a closed contact $3$-manifold. Let $(\lambda,J)$ range over ECH data for $(Y,\xi)$, and let $f(Y,\lambda,J)$ be the invariant defined in the paper. Converse overtwistedness conjecture. If

$$f(Y,\lambda,J)=0$$

for all ECH data $(\lambda,J)$ for $(Y,\xi)$, then $(Y,\xi)$ is overtwisted. This is proposed as the converse of the result that overtwisted contact $3$-manifolds have vanishing $f$ for every ECH datum. The source also notes that it would imply the conjecture that Legendrian surgery preserves tightness.