Do you think any fans of the various clubs who have gone under and been reborn feel like they've transferred allegiance? I doubt it. I also suspect that with a strong campaign in the city and serious backing a large majority of fans would prefer to support the new club.
I still feel like the various conversations that are happening about a new club are lacking in focus here, though. Lots of people are sceptical about it working (which is fine, nothing is guaranteed) or being a good idea (also, there's no way of knowing it it really is the best path yet), but I think we ought to start polling for the most important things that fans want to see in a new club. The values of the club, how it's organised (we don't want to ever find ourselves in this situation again, do we?), how to finance it etc. etc. I would still prefer the club to be named ‘City of Coventry Football Club’ rather than ‘Coventry 1883’, for example, but I'm sure that's nowhere near as important for everyone.
So how about that — focus on adding your tuppence on what you'd like in a new club, rather than debating if it should/could even happen?