[MLD-Grounds-Keeper-Willie]

I think that boromir would have taken the ring to minas tirith and repel the orcs. He would have stayed strong against the ring's will but it would still be growing on him. He would realize this and would decide to destroy it himself rather than give it to anyone else. He would have made it to Mount Doom and had a great struggle to destroy it but in the end, he would destroy it. He would be exhausted and left weak-minded lying on the floor of Mount Doom. MD would explode and boromir would die.

However, before Boromir could get that far, Aragorn would stop it. He would not want to have Boromir use it so he would claim his kingship over gondor and demand boromir to hand the ring to him or Frodo. after that, I don't know.