Yes and No
Some instructions must be restricted to the kernel, e.g. configuring the MMU.
When a privileged instruction is executed, it causes a trap (exception). This trap can be handled by the kernel. The kernel can choose to run the instruction on behalf of the user-mode-process (possibly after checking and sensitisation).
On the x86, some privileged instructions are not privileged, so don't trap. They do however give the correct answer. This can be a pain for virtualisation, when virtualisation privileged code. (E.g. asking what mode am I in, and being told user-mode).