Legal Question in Business Law in California

Yes

Yes, the potential of criminal fraud charges if the business is operated for improper purposes.

This is like asking "Are there any legal ramifications of my buying a carload of ammonium nitrate?"

If you are growing cotton in a nitrogen-deficient area of Mississippi, the answer is no. If you are planning to blow up the Murragh Federal Building in Oklahoma City, the answer is YES.

Before becoming a lawyer, I was an entrepreneur, and I have had occasion to use secretarial services to forward mail to my home address in California while setting up the appearance, at least, of a local presence in New Mexico or Washington.

This was to show commitment to the project, and was always accompanied by setting up a new corporation in the target state (NM, WA, etc.). There was never an intent to avoid taxes or conceal where I lived.

So, I think the issue is not that I am in State X and my mail is directed to State Y and then forwarded to me in X so much as it is whether the intent or effect of the setup is to cheat or defraud anyone.