: There is, of course, no "right" answer, but I'm curious about how many different perspective people may have on this. I suspect he would have gone on to Minas Tirith and sacrificed himself somehow, but then his death would be less tragic.

Firstly, the panic at Rauros would still have happened after Frodo's disappearance, so I would imagine that Frodo and Sam would still have set out for Mordor on their own. However without Merry and Pippin there would have been no need for the mad dash into Rohan, the remaining members of the fellowship would have probably set out for Minas Tirith directly.

Without the aid of the Ents (unless the rebodied Mithrandir would have been able to rouse them in time), Rohan would have fallen with Theoden, Eomer and Eowyn dying at Edoras or possibly at Helms Deep (again putting responsibility on Gandalf for rejuvinating Theoden and organising some resistance at the Hornburg). If this had happened, Saruman's forces would have attacked Gondor from the West. In addition there would have been no reinforcements for Gondor from Pelargir and the southern fiefs as Aragorn would not have been able to ride the paths of the dead and Gandalf would have been unable to make it to Minas Tirith. Aragorn would not have challenged Sauron via the palantir of Orthanc and so the Dark Lord would have been able to take his time and not hurry his stroke.

Without the aid of the southern fiefs and the ride of the rohirrim, Minas Tirith would have fallen, despite having Aragorn in the citidel. The presence of the putative king would probably have caused dissension within Gondor, a stronger Denethor aided by the presence of his favoured son would possibly have clung on to his seat longer.

In the event of Minas Tirith falling, and presuming that Boromir did not die gloriously during the battle, they would have retreated into the fastnesses in the mountains and so would have fought a kind of long defeat.

In any event the Dark Lord would have eventually won, possibly recovering the ring in the process as his attention would not have been distracted by either the disaster (from his point of view) at the Pelennor or Aragorn's maneouverings afterwards in Ithilien and Dagorlad.

In whatever case Boromir's death whether at the siege of Minas Tirith or later fighting in the resistance would have been pointless and irredeemable. The presence of Merry and Pippin allowed the only fitting death for Boromir. In my opinion, his dying at that particular place and time was his wyrd, his fate and probably the best thing he ever did.