I've seen plenty of teardowns of drives from Seagate, WD and HGST and they all use a foam pad to isolate the PCB from the metal case.
The only drives that actually shielded the PCB was Seagate many moons ago with their Seashell on the barracuda drives.
I still have one, PATA 80GB.
Unless a thermal pad was used to cover the chip it would reduce flow and thus increase heat.
A cover is not going to help with a voltage spike, only handing of the drive and ESD.