No, but the data (zero and ones) representing the gates must be processed by the CPU for the emulation to take place. It’s the CPU that performs the emulation by processing that data. And the emulation is much slower than the actual electronic circuit.
So if you want to emulate a CPU, you still need a real CPU that does the emulation, and the emulation will (usually) be slower than actually running the emulated CPU for real.
For example, you can emulate an Intel CPU on an Apple CPU (or vice versa), but that emulation may be slower than if you had a real Intel CPU (or real Apple CPU) in the first place.
In any case, you can’t emulate CPUs out of thin air, i.e. just with storage.