[Boromir88]

Also, I doubt Aragorn would have let Gollum come with them to Mordor.~Menel

And there's the key, Gollum is the reason the Ring is destroyed. As we are told the Ring was beyond the strength of any will to injure it or cast it away, and in Letter 246 Tolkien says it was impossible to resist the Ring at the maximum point of influence in the Sammath Naur. Then as Letter 192 points out, it is Eru who steps in and intervenes to destroy the Ring:

Frodo deserved all honour because he spent every drop of his power of will and body, and that was just sufficient to bring him to the destined point and no further. Few others, possibly no others of his time, would have got so far. The Other Power then took over: the Writer of the Story (by which I do not mean myself), 'that one ever-present Person who is never absent and never named' (as one critic has said)

Even though if Eru does decide to get involved, it was because of Gollum, as Gollum was problem the biggest influence if only for Frodo's sake. Letter 192 is often taken out of context and you don't get the full meaning unless Letter 181 is quoted with it:

’But at this point the ’salvation’ of the world and Frodo’s own ’salvation’ is achieved by his previous pity and forgiveness of injury. At any point any prudent person would have told Frodo that Gollum would certainly betray him , and could rob him in the end. To ’pity’ him, to forbear to kill him, was a piece of folly, or a mystical belief in the ultimate value-in-itself of pity and generosity even if disastrous in the world of time. He [Gollum] did rob him and injure him in the end- but by a ’grace’ that last betrayal was at a precise juncture when the final evil deed was the most beneficial thing anyone could have done for frodo! By a situation created by his ’forgiveness’ , he was saved himself, and relieved of his burden.'

Without Frodo's act of pity towards Gollum I doubt Eru would have intervened to destroy the Ring. Pity and Mercy are big themes throughout the book, and it was Frodo's previous act of Pity when Eru decided that Frodo deserved salvation and deserved to be relieved of the Ring, so he intervened and caused it's destruction. If Aragorn goes along, you're probably right Menel, he would not have allowed Frodo and Sam to take a long Gollum, in which case, how does the Ring get destroyed? As then there would be no act of Pity towards Gollum, by Frodo, and his 'salvation' would not have taken place.