Define "iconic" in your own words.
Because I'm not entirely certain that that word means what you think it means.
He's iconic in the sense that he conforms to the traditional cowboy character archetype. He's a tough, gruff, somewhat laconic, no-nonsense gunslinger who slings guns, rides horses and wears a hat. He could easily have been played by Clint Eastwood.
I'm not so sure that he iconic in the sense of being the quintessential video game cowboy. If only because there aren't that many video game cowboys around.
Recognizable? Uhh... sure? I mean, I recognize him. Damn near anyone who's played the game will recognize him. If you mean recognizable in wider culture then no, fuck no. He's utterly unknown outside of gaming.
Enduring? No, not really. When it comes to video game characters, longevity is based at least somewhat on reoccurrence. Lara Croft is iconic at least in part because she just keeps bloody coming back. She stays fresh in the memory. Same with, say, Mario, who has been getting games for like 30 years now. Mr Marston got one game and presumably isn't going to be getting another. He'll be forgotten along with his one game. Red Dead Redemption was a passable game I suppose, sold well, reviewed well and all that, but it was hardly an unforgettable classic that will loom over the medium for many years to come like, say, Doom was.