Yes, and to be more clear, in order to do something like this, you'd need to manufacture a chip to do so. It doesn't have to be a full CPU, but it does need to intercept any signal looking for the id and pass the rest to the real CPU you're using. If there's any cryptography involved, the problem becomes NP hard to solve unless you can get ahold of a private key, but then you might need to intercept even more signals to keep everything coherent.

And you need to solve any problems involved in having two chips (or more) work together seemlessly. And if you want to fit it on one package, now you need to make a custom one that routes the pins as you need them to be, when the current design already tries to make optimal use of the space. If you could do this, you could probably make more money working with one or more chip makers legitimately.

Odds are all of this will be more expensive than the difference between the price of the high end chip you're pretending to be and the low end chip you're really using. Unless you can sell them at a scale that will attract the attention of the companies that you're trying to steal revenue from who have the tools to make detection easy regardless of what your custom chip does.