Everyone’s focusing on the “Bray” part of this question, but Jim does couch it with “e.g” and in the larger context of “range” and “one or more requirements.” Thus I interpret this question as “Could anyone else have managed the romance with Tracy, the grief of losing her, the Bray imposture and the action all in one film, better than Roger?” That to me is a different question.
I think Roger could easily have beaten Connery in selling a Bond capable of falling in love, at least if OHMSS came first in his run. Once his true tenure got underway no one seems more callous or misogynistic than early phase Roger-Bond, but later we can believe he feels real tenderness towards Melina, Octopussy and maybe even for some unfathomable reason Stacey. The proposal scene would’ve been great in Roger’s hands, and maybe losing Tracy would even help explain why he turns into such a cad in LALD and TMWTGG. Roger also could have aced Tracy’s death scene and it would have added weight to her mention in TSWLM and the cemetery visit in FYEO. Having said all that, Laz does surprisingly well with this material and his inexperience somehow projects a youthful vulnerability that really helps, if only perhaps by accident. I could also see Dalton handling it very well.
Obviously Roger could have sold the fatuous functionary disguise as Sir Hillary, so I’ll give him the nod there, as well. But here’s where we start to get into trouble: audiences seemed to have already been uncomfortable with all the things Lazenby was asked to do in this film: he had to fall in love, get his heart broken, suffer a crushing defeat, pose as a nerdy and possibly gay bureaucrat, etc. Lazenby exudes enough of a macho vibe to survive most of that, and anyway he never returns so there’s no “image” to preserve. Roger on the other hand would have been starting out already prettier, more “mannered” and “posh” and aristocratic than Sean or Laz, without their vibe of “I may be wearing Saville Row and sipping champagne but underneath I’m a brawler.” If he’d had to spend so much time in the Bray persona – in his first ever appearance as Bond, mind you – I think it could’ve made him seem too soft and poncey and made it harder for audiences to cope with the whiplash of the transition from Superman Sean to .Mushy Moore.
Years later, Roger-Bond would pose as the effete upper class twit James St John-Smythe and it’s disconcerting for me to watch because he seems more comfortable and natural in that skin than Bond’s. Similarly, after I saw Roger in “The Naked Face,” where his only “fight scene” is a one-sided beatdown where he’s pummeled to a pulp, I realized it was more believable than most or all of his Templar/Bond fights and I could never see those the same way again.
All of which is to say, could Roger have done all that OHMSS asked of an actor? Yes, I think so. But would it have been a smart way to start his tenure? Possibly not. Much as I love Roger – and he’s still my favorite Bond – a certain amount of deck-stacking needs to be done to make him work as an action hero capable of holding his own against the physical powerhouses he often faces in his adventures. A lot of OHMSS is about stripping away the “superman” persona to reveal the human side of Bond, while I would argue Roger needed the “superman” elements propped up under him, not pulled away.