Yes, I see no reason to assume that Joe Buck would not be able to get his life together after moving to Florida.
He was naive and of sub-normal intelligence, yes. But - consider this. He was able to get through his experience in New York without developing a drinking problem or a drug addiction. He did not lose his physical health; he is still young and strong at the end of the movie.
Moreover, he relocated to Florida. The New York that he left was an absolutely miserable, soul-crushing place, and not somewhere where you would have an easy time making a new start of life even under the best of circumstances (high education, social connections, a good source of income.) Being a gardener or construction worker in Florida would have been a life he could have adjusted to without too much trouble, and he seemed ambitious enough to make it work.
I have a feeling that if he just went around offering his services as a gardener or groundskeeper to a bunch of elderly women in Florida, he probably would have done OK. Also, there are shitloads of golf courses there that he could have done landscaping for. I think he would have done OK. Of course, since the character of Joe Buck begins and ends with Midnight Cowboy, it’s pure conjecture. But I’ve known real-life Joe Buck guys. The thing that always fucks them up is getting into drugs. Their guileless charm and good-natured ambition don’t mean much if they’re always too fucked up to work, and/or in jail.
But again, Joe Buck didn’t seem like he had an addict’s mentality, and I don’t see him going down that path, at least as the character is portrayed in the movie.