The exposed silicon die that you see with your eyes is actually the backside of the CPU, itself hermetically sealed with a silicon nitride layer so the bare silicon is not exposed.
The layers of concern that you are thinking about are safely hidden away by being mated (soldered) to the PCB layer.
That said, you do not want to press a small hard ball into a brittle material. In Materials Science we do this as a standard test for determining a material's
fracture toughness and hardness.
The diamond paste will act as nanoindentors, the overhead IHS will act as the downforce, and the silicon die will become the "specimen under test". Silicon does not have a good fracture toughness.
If the nanoindentors (the diamond particulates) are smaller than the gap between the IHS and the CPU then the downforce transmitted from the IHS through a diamond particulate and into the silicon will be negliable, no concern then.
But I would not do it on a bare exposed die without the aid of mechanically robust standoffs. I've done those tests in college and at TI with
Knoops hardness test and
Vickers hardness test machines, and the outcome is always the same - test ends with mechanical failure of the specimen under test