In editor, place a player, name it;
place a backpack ("B_AssaultPack_Kerry" in this example);
place a mortar unit, name it;
place a module requester, name it (say request);
place a module provider artillery, name it (say arty);

synchronize request to player and arty to mortar, let unsynchronized arty and request as scriptable sync.

in init.sqf (or elsewhere), add this loop:
player spawn {
_unit = _this;
while {true} do {
sleep 2;

  waituntil {sleep 2; (backpack _unit == "B_AssaultPack_Kerry")};
    if !( request in synchronizedObjects arty) then {
     arty synchronizeObjectsAdd [request];
     hint "support added";
    };

   waituntil {sleep 2; (backpack _unit != "B_AssaultPack_Kerry")};
   request synchronizeObjectsRemove [arty];
    hint "support removed";
    };

};

The hints are toggling while taking/dropping this backpack but you can get the support only the first time you take the backpack.

Same problem in SP/MP missions than preview, with any type of support (virtual or not) any kind (CAS, artillery, drop...).

You can verify the syncs with a hint format ["%1", synchronizedObjects request] or arty. Syncs are all present with backpack and arty-request truly removed after dropping the backpack.
So, commands seem to work but support is no more in menu.