[ruelnov]

No.

When capacitors give in, the hardware monitor chip automatically shuts off the system by asserting a RESET signal to the processor and other micro-controller chips.

If the processor becomes busted, then that's a failure of the thermal sensing circuitry (if that board is provided with one). Some low-end boards are not equipped with this functionality.

On motherboards equipped with fail-safe thermal sensors, the processor automatically goes to SLEEP mode on overheat and so procesor damage is prevented.