Compact integration criterion for Poisson linearization around symplectic leaves

Let $M$ be a manifold with a Poisson structure $pi$, and let $S\subset M$ be a compact symplectic leaf. The restriction $T^*_S M$ is the cotangent Lie algebroid along $S$.

Poisson linearization conjecture. If the restricted Lie algebroid $T^*_S M$ integrates to a compact, source 1-connected Lie algebroid, then $pi$ is linearizable around $S$.

This is motivated by Conn's linearization theorem and asks for a leafwise analogue in the sense of Vorobjev. The source presents it as a conjecture and gives no resolution.