The point that Tolkien is making in Letter 246 seems to be that no one (and certainly no one who had carried the ring all the way to Mount Doom) would ever have the psychological strength to give up the One Ring, there in the Cracks of Doom where it was wrought and its power was the strongest. For a weak creature like Gollum, it would actually be much easier to throw himself into the fire, rather than face giving up the Ring again. And perhaps even Frodo would despair and (having claimed the Ring but with the imminent prospect of losing it to the minions of Sauron) decide, "If I cannot have it, no one shall!"—then dive headlong into the Cracks.
By destroying the Ring, this would also destroy Sauron's power, and so it would be a victory of sorts—although not for Frodo personally, since suicide is a mortal sin in Catholicism. Having taken his own life, Frodo's soul would still be damned (whatever exactly that means in Tolkien's universe) once he passed beyond the circles of the world. It might seem extraordinarily unfair to Frodo for a benevolent Ilúvatar to place him in this position—where he cannot resist the strength of the Ring's attraction, nor can he destroy it without also destroying himself. But it is precisely to free Frodo from this unfair choice that Providence may have provided another way out of the situation.
Note also that, in Letter 246, as in many others, Tolkien treats himself as the interpreter of the works he has created, not an oracle. He talks about what he intended to convey as an author, or what he thinks might have happened, had events in the story gone differently. However, he does not make a lot of firm pronouncements about what would happen in counterfactual situations. Those do not correspond to the story he wrote, so he can guess how he might have chosen to make it turn out—but it is just an informed guess. Tolkien points out in a footnote that he changed his view of how the climax at the Sammath Naur should play out multiple times while he was working on The Lord of the Rings, and only when the story actually reached that point was he able to provide what he decided was the "correct" climactic encounter. Had he built up to the climax differently, a different ending—with an entirely different logic to it—might have been needed.