Hi AslansCompass,
I think it sort of depends on what Boromir 'knew' about what the Ring was from the beginning.
At the Council of Elrond, all the participants, including Boromir 'know' that if Sauron regains the Ring he will be invincible. So it is critical to keep him from getting it. They also 'know' that there is a danger in trying to use the Ring as a weapon against Sauron, as the wielder would become a new Dark Lord. (It is not exactly clear where this 'knowledge' ultimately comes from. It does not seem to have been 'known' to Elrond and Cirdan when Isildur claimed the Ring, that a wielder might become a new Dark Lord. It is obvious that Sauron gaining the Ring would be disastrous, mainly because the wielders of the Three would fall under Sauron's power.)
At any rate, Boromir learned all these things during the Council, at the same time as most of the other participants, and I'm not sure that knowing some things about the Ring earlier would have affected the Council much.
The one thing that might have changed the course of events is if Boromir had known that destroying the Ring would destroy Sauron. No one knew this at the time of the Council. It is only at the Meeting of the Captains of the West, after the Battle of the Pelennor Fields, that Gandalf suggests it. How did he know by then? Maybe he got the info in the process of becoming Gandalf the White?
If Boromir knew that destroying the Ring would destroy Sauron, he might have been more positive towards the quest for Mt. Doom? Great risks for great rewards might appeal to Boromir more than great risks just to deny Sauron the Ring, leaving him still as an extremely dangerous and deadly threat to Gondor.