While a corporation may be qualified to do business in any number of states, a corporation can only be incorporated in one state. I therefore assume what you meant is that the corporation is qualified in a number of states.
Why?
You can buy all the property you want (subject to your financial ability, of course) and set up a mailbox anywhere you like. Having your mail delivered to an address in a state where you don't live seems pretty dumb, but whatever floats your boat. You can't legally get a driver's license in a state where you don't live. All that said, I'm not sure what this question has to do with the rest of your post.
If you're wondering whether doing these things will satisfy the potential employer's request that you "relocate to a state [in] which [it is qualified to do business]," I would suggest asking your contact with the company.
What law? What "legal/tax concerns"?
Perhaps qualified is the correct term, I'm just using the phrasing that the recruiter used.
My presumption was that they were incorporating or creating an organization within each state as protection to the parent company.
Why relocate? Per the recruiter, they only hire within the states in which they are "incorporated".
I don't know what law(s) or tax concerns they're trying to satisfy.
What you'd be doing is deceiving them about where you actually reside, which is not compatible with your stated desire to "to achieve the minimum required to be within the law so that the employer's legal/tax concerns are satisfied". Instead, you'd potentially be committing fraud as to your employer and, depending on exactly what you do, may also end up committing tax fraud as well.
Instead, be upfront with the potential employer and ask if there is any option available for you to be able to work while living in another state.
My goal in this forum is to determine if there's a feasible way to satisfy the residency issue in a legal and tax compatible way, while keeping my NC residence.
I'm only in the 2nd round of 6 rounds of interviews, so if I can't figure out a way to make this happen, then I need to exit the interview process early, as I'm wasting my time and the employer. I'm running this possibility down as I'd floated it by my recruiter, and he said "unofficially" if I could make it work, fine with him.
Actually moving isn't an option as my wife works on-site where we live, and I don't want to interrupt her career.
If this solution is feasible, then I'd make sure the company was aware I'd be using relocation funds to basically establish legal residency in VA while retaining my NC home.
Be aware that if you go the route you plan, you'd be setting yourself up for tax problems as the employer would be withholding and reporting employment taxes for you as though you are a resident of VA. Even once you straighten out that with the states involved, you'll be filing two state tax returns every year if the work you do is actually in VA. VA has the right to tax you due to working in the state and NC has the right to tax you as a resident of that state. NC would give you a credit for the tax you pay to VA, but if the VA tax rate is higher than NC you still end up paying the higher VA tax.
I'm not too concerned about the higher tax rate.
Per the recruiter, he's pushing for the company to add North Carolina as another "incorporated" state. It's a slow process apparently, so my goal would be to use this process to get through a year or so until they properly have a presence in NC.