[Boromir88]

Orophin:

Do you really think Aragorn could have killed Boromir while he had the ring? Possibly.

I think Boromir could have been a challenge to Aragorn even without the Ring. Aragorn in the end is probably the better swordsmen, but Boromir wouldn't be a pushover, anyway that is off topic, and my speculation.

So, on topic....

Elessar:

Also, I feel he would turn on his father when asked to give up the Ring and possibly feel paranoid towards Faramir. The Men of Gondor would be most likely to side with Boromir and thus would cast Denethor out of their lands.

I tend to believe differently. If Boromir had made it to Minas Tirith, his sole purpose in claiming the ring was to save Gondor, he thought it could save Gondor, and that's the weakness the Ring attacked in Boromir.

The Council of Elrond:

"I do not understand all this," he (Boromir) said. "Saruman is a traitor, but did he not have a glimpse of wisdom? Why do you speak ever of hiding and destroying? Why should we not think that the Great Ring has come into our hands to serve us in the very hour of need? Wielding it the Free Lords of the Free may surely defeat the enemy. That is what he most fears, I deem.
"The men of Gondor are valiant, and they will never submit; but they may be beaten down. Valour needs first strength, and then a weapon. Let the Ring be your weapon, if it has such power as you say. Take it and go forth to victory!"

Boromir could not have been more wrong with that statement, but the words I underline would seem to me like Boromir didn't wish to claim the Ring for himself. He very well could be hiding his true thoughts, but I don't think Boromir would have become hostile to Denethor or Faramir if he had reached Minas Tirith. I believe Boromir did want the Ring for himself, but I don't see him becoming hostile towards his family, if Denethor asked for the Ring, Boromir would have given it to him.

I agree with Mithalwen's point, Boromir would have met the end like Isildur, and would have never made it back to Minas Tirith.

There is an interesting bit that I would also like to mention. In one of Tolkien's earlier drafts he actually had Boromir join league with Saruman. Which case, Boromir and Aragorn go to Minas Tirith, Boromir stirs an uprising and Aragorn has to kill him. Your thoughts on that? And I wonder why Tolkien abandoned that idea? (I happen to like the "final" Boromir better, lol).