I vaguely remember doing this in the past, when I did not notice that the HQ was in the city before I razed it. I think that the result was, without the HQ, no one got the income from the Corporation. However, the other cities where the Corp had spread still got the benefit from the Corp (for example food and culture from Sid's Sushi) and could still build Executives to spread the Corp further. The HQ could not be rebuilt anywhere.