The same restriction that makes the brick menu show "building is disabled" also disables using the brick cart.
It'd be possible to disable getting bricks from the menu, though, and I think force-adding them to players is possible in a similar way to items.
There should be a "uses" field for addBrickToInventory - can you use a brick infinite times (v0002), 10 or so (RPG games) or once (deathmatch/competition).
Player -> addBrickToInventory
Player -> clearInventory
fxDTSBrick -> setBrickBuildable
Minigame -> ClearAllTempBricks (deletes all bricks placed via addBrickToInventory)