OK, back to Boromir (I'm almost happy that the guy is going to be dead soon. . .oops. . .did I type that. . .?
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I think that it might be a bit of red herring trying to ferret out whether he is "addicted" or "tempted" or "corrupted" or what have you by the Ring. Not that it's a useless endeavour, far from it as the discussion is illuminating, but I rather think that perhaps Boromir's fate in this chapter, which concludes the long sweep of his characterisation right from the Council of Elron, deserves a more subtle and complex form of understanding. That is, there is no single or easy answer to what 'happens' to him with the Ring. Which is why I always like to see him as a tragic hero.
Now, he is not as 'successful' a tragic hero as the really great ones (he's no Oedipus or Hamlet, that's for sure), but a tragic hero he remains. The basic definition of a tragic hero (get ready to write this down for future reference) is someone whose greatness is his own downfall -- that which makes him a hero is what dooms him to destruction and perhaps even villainy. Oedipus, for example, is a restless solver of riddles, he finds things out. Had he not been this way he would never have gone after the truth of his birth so relentlessly, and never would have found out that he's married to Mom after killing Dad. Hamlet's the other great example. He is a thinker of no small measure: he is brilliant and moral and possesses a capacity for understanding that goes beyond anyone in his world. Because of this, he is too aware of the implications to what he is supposed to do -- he knows that to murder Claudius is to commit a sin, whereas leaving well enough alone is also a sin. He tries to find some way to do what he has been ordered to do, without creating more problems. It's an impossible situation and he knows it, and this is what makes him great and doomed.
So on to Boromir. His greatness is his heroic stature among Men. He is a hero and unproblematically so. He is great and noble and smart and strong and honourable -- it is his tragedy that he is drawn to the Ring for all of these reasons. I don't think that we need to start going into a search for the "flaws" in his character that lead to his destruction, since the Ring plays on his strengths. He is a military commander of no small measure, a leader of Men, and totally devoted to his kingdom. These are the things that the Ring offers him, and he falls.
So all this gets into the disturbing ambiguities that beset all tragic heroes. Does his fall mean that his values are wrong or 'bad'? Is his mode of heroism being undercut or devalued? I don't think so, since Aragorn, Eomer and Faramir are going to be doing a lot of leading and killing and fighting of their own soon enough. Does his fall mean that he isn't really great or heroic at all? Again, I don't think so -- if he weren't such hero, he would not have attempted to seize the Ring, as he would not have desire to save his city.
The thing about effective tragedy is that it makes us uncomfortable, I think. There are two reactions to this discomfort. The natural response is to seek easy answers with which to do away with the discomfort -- these easy answers usually take the form of some kind of distancing between ourselves and the tragic hero: he is 'flawed' in some way that we can identify and safely categorise and say we are not flawed that way (Hamlet "thinks too much" -- a ridiculous idea, as in the play it's when people don't think that they get into trouble). Boromir is "proud" or "arrogant" or somesuch -- but he is right to be proud: proud of himself and of his achievements, proud of his land. It is because of this pride that he has come on this journey and suffered along with the rest. But it's because of this heroic pride that he falls to the Ring.
Like all tragic heroes, Boromir is neither good nor bad, right nor wrong, perfect nor flawed. And he's not all of those at once. He's just human, which is to say he is what he is, and there's nothing he can do to change that.