Not exactly. They sent the guy who controls the local judiciary because not doing so would be impossible due to his immense political power. The Israeli judiciary is unique in nominating itself and having given itself the power to cancel any law or demand any changes to laws/policy on any arbitrary basis; since this state of affairs is backed up by a sufficient number of powerful institutions, it is effectively impossible to challenge.
Barak ruling to resupply the enemy (it is widely documented that "humanitarian aid" goes first and foremost to Hamas) in an international court is entirely consistent with his lifelong tendency to gradually reduce Israeli independence and voters' impact on policy and to increase Israeli compliance to the policy of outside parties, first and foremost the US. (Resupplying the enemy was required by the US from the start. It is interesting to see other examples where civilians are prevented by the international community to leave the area of hostilities and instead they are supposed to be provided with resources in this area where the monopoly on the use of force belongs to one of the sides in the conflict.)
While the exact requirements placed on Israel by larger powers are somewhat unique, having highly influential people in the country effectively work in the interest of larger powers is a common condition for smaller powers. In this Barak is similar to many other high-profile people and organizations in many other countries enjoying limited sovereignty at best.