Would winglets add fuel efficiency on a Concorde?
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.