Would adding winglets to a Concorde have a had a positive impact on its performance and fuel efficiency in retrospect, considering the technology was not widespread or developed at the time these machines were flying and would that at all have reduced/increased its sonic boom?
The answer is no and the airplane in question is intentionally designed this way.
Standard sweptback wings produce the characteristic vortices st the wingtips. The concentration of these vortices at this point in combination with little lift being produced by the vortices makes a singlet an effective feature to reduce induced drag. Delta wings on the other hand produce vortices along the entire length of the wing, particularly at low speeds and high angles of attack. Concorde designers took this into account in order to produce better low speed handling characteristics as well as the olgive delta wing provides a very clean high speed wing. The wing was one of the most heavily researched and planned features of the jet during development.
The upshot of which is that adding winglets onto a Concorde not only is fairly ineffective way to reduce wingtip vortices and induced drag but impinges upon low speed flight capabilities, requiring greater takeoff and landing rolls and high approach AoA.
No they would not.
Winglet technology for supersonic aircraft was already a known factor when Concorde was designed. The XA70 Valkyrie Mach 3 bomber prototype first flew in 1964 and had folding down wingtips: extended during subsonic flight, folded downwards like winglets during high speed supersonic flight, for increasing lift by riding the shock waves. The Concorde designers had their own elegant solution to merge high- and low speed requirements in the wing design, in which winglets had no place.
The sonic boom shocks form at every point the airflow hits the aircraft structure, limiting the magnitude on the ground is more a matter of spreading the shock wave out.
The magnitude of the sonic boom depends mainly upon:
- Length of the aircraft, the shorter the louder.
- speed of the aircraft, the closer to the speed of sound the louder.
- Altitude of the aircraft, the lower the louder.
None of these factors are influenced by the addition of wingtips.