I get tired of this, as I do answer but, seemingly, my answers aren't acceptable. I could bang on about reading formation theory, and how certain strategies are used to position entities in a particular way. I could bang on about inter-textual strategies. I could bang on about authenticity as a social construct and a shared system of belief along with audience response, and the battle for status within fan cultures and subcultures but... that would be rather boring, and I have neither the time nor inclination to an unreceptive audience.
I can say that if Coventry Sphinx were considered to be the club that people saw as continuing the Coventry City legacy, then that would be it. It's highly unlikely that would happen however - may as well ask what would happen if pink was green. The evidence is there of previous clubs what happens, and how the fans consider *their* club to be *their* club. There's no reason as it stands why Coventry Sphinx couldn't become the dominant club in the city, anyway... but that's a whole different issue and digression.
Of course some fans would drop by the wayside at the point of oblivion, that's only natural. Ultimately, however, it's cultural appropriation, and that's nothing that SISU haven't (tried) to do already, anyway. Some would be passive but return at success, some would go completely, new fans would join and be told of the FA Cup win - it's nothing that doesn't happen now.
Also, what doesn't happen, is two clubs are formed. May as well ask what happens if twenty two are formed. For examples and evidence based about the battle for that cultural authenticity, then you can see how destructive the battle for Enfield is and was, when a rival club was formed when the present one still existed. Similar has happened at Northwich, but I don't know enough of that to say with any authority how that has panned out to date.
As mentioned, it's all a little irrelevant while CCFC exist. As also mentioned, it's only wise to have a contingency. As also mentioned, this was an aside so in the interests of focus I'll bow out, as I( just don't have the time to bash my head against a brick virtual wall.