Left unstated is that the Concorde was designed at a time when aviation gas EDIT jet fuel ENDEDIT was priced at pennies per gallon.
That said, it might still be flying if its recertification flight hadn't happened on 9/11.
I'd guess not. It was aging, maintenance was getting ever more expensive, Airbus didn't really want to support it anymore, and it faced ever more competition from better first-class amenities on regular planes, and from the internet reducing the need for fast business travel. It was modestly profitable in its heyday once the capital costs were written off, but it didn't have a lot of headroom.
Jet fuel cost about $1/gallon when Concorde retired. Five years later, it would hit $3/gallon. I have to imagine that would have ended it if nothing else had by that point.
I'm relatively certain that neither Concorde nor any passenger jets burn aviation gas. It may be physically possible, but would be extremely ill advised given the lead additive