Diablo, the small adhesive attached BGA heatsinks weigh almost nothing. They're not going to stress the chips.
But are they going to help? BGA cases are flip-chip; with chip substrate connected to the top of the case.
QFN packages don't flip the chip and actually have air between the top of the package and the chip, because they need to accommodate the bonding wires. They really want to be cooled through the bottom of the PCB because this is where they have the least thermal resistance and a biggest piece of metal: ground connection for the substrate.