Very unlikely.This Doctor William Adair was born in about 1705.His death was registered in May 1795.Listed under burials in Vol 1 of the Queen’s Chapel Archives (still in Gibraltar): "William Adair MD Surgeon Major of this Garrison, aged 90."
Genforum 2941 states: Gentleman's Magazine (per 050G) 1795.page 614. June 14 1795 (but perhaps that was the date of publication?): "Death at Gibraltar, William Adair Esq. late Surgeon General of Garrison there."
I have found other references to him in the handwritten minutes of the Garrison Library, Gibraltar:
Wed 31 Jul 1793.General Meeting in “the Hotel” to set up the Garrison Library, amongst them Sgn Major Adair.
Wed 4 Sep 1793.Sgn Major Adair (Staff, Civil & Ordnance Dept) having however unexpectedly declined acting with the deputation (assigning as a reason his age and profession).The committee came to a resolution that they were competent to act, notwithstanding Mr Adair’s secession [= act of withdrawal or retiring], and immediately proceeded to elect the 10 additional members from the subscribers at large, leaving Mr Adair’s vacancy to be filled hereafter by the departments he represented.[He was replaced by the Rev Mr Hughes].
This Surgeon Major Adair would appear to be the Surgeon Major William Adair listed in the 1791 Army List, and possibly the same Surgeon Adair on half-pay at the Havannah in the 1785 Army List: "Surgeon William Adair at the Havannah" (p332) (the Havannah [now Havana] in Cuba was captured by the British from Spain in Aug 1762).