Well, yes, but as your hesitancy suggests you already know, none of the men in the novel really embody these ideals powerfully.
Dr. John Graham Bretton is good looking, and has the striking eyes of the Byronic hero. He also has a bit of deception about him, living more than one life, and that's part of the gothic tradition that overlaps with Romantic fiction. However, he's a little flat to be a full-blown Byronic figure. (He's also a bit too honorable.)
Colonel de Hamal is considered a man of sense, which is period ideal, though not Romantic or Byronic.
M. Paul Emanuel's passion does work as a Romantic figure. Likewise, the fact that he is forced to an alien land (the West Indies) fits him as Romantic, as do some of the forces working on him.