I don't see Ennis as QUITE as screwed up as some people do. He's shy and inhibited and hot-tempered, but those are fairly ordinary traits that don't necessarily preclude happy relationships. The only really big, relationship-hindering problem Ennis has is homophobia -- as long as that was an obstacle, he'd never take Jack up on his idea. In the actual movie, it took Jack's death to show Ennis that he shouldn't have let homophobia get in the way of their happiness. Once Ennis gets that, his attitude is much better; if he had it all to live over, I'm sure he would have done things differently.
So RT's question requires assuming that some other event or epiphany caused Ennis to see the light sooner. If that happened, then, yes, I think they could have had as much chance as anybody to succeed as a couple. More, in fact, because their personalities and skills are so complementary, and because their relationship was SO GREAT in so many ways.
And Scott, thanks for pointing out that
By the end of the story, a remarkable number of people know (or knew) the truth about Ennis and Jack: Aguirre, Alma, Mr. and Mrs. Twist, Lureen, and possibly Alma Junior. And Ennis is still alive at the end.
I've always really liked that, because it adds another layer of meaning. As we all know, in real life Ennis' fears are not unfounded. But in the movie itself, nobody who is aware of their relationship does anything mean to them at all, outside of a few snide comments. Aguirre doesn't even do that until a year later! Alma waits until long after their divorce! By making Ennis' hangups the most serious obstacle, the movie becomes not just about the life-choice limitations imposed by an intolerant society (which, IMO, better describes the short story), but also about how that intolerance warps its victims emotionally, and about the broader issue of not letting your fears rule your life.
(BTW, somewhere around here I saw someone who sounded pretty knowledgable about ranching describing all the economic factors that would have made their success unlikely. If I find it, I'll let you know.)