And perhaps *except* Frodo's mission (and its outcome?) would have been altered. Certainly, Aragorn could not have made it to the Mountain of Doom in the manner which Frodo and Sam did. Nor would the capture of Frodo been treated as cavalierly by the Orcs had Aragorn been present (either he or Sam would have been found as well, since only one could wear the ring). His presence could have caused the ring-bearer's mission to go awry in a number of ways.
Maybe that was part of what his "heart" spoke so clearly.
I wasn't really addressing the effect of adding Aragorn to Frodo's quest so much as the results on the West -- on Gondor and Rohan.
Adding Aragorn would have doomed the Quest, as you have said. That seems almost certain. Aragorn wouldn't have done the things Frodo did and wouldn't have made Frodo's 'mistakes' (such as going to Shelob's Lair and taming/trusting Smeagol). These apparent mistakes ended up being vital to getting the Ring to Mount Doom.
Tuor