Seeing as how we only have knowledge of the past and present, I have to say "I don't know and neither do you". Even if he was caught, that wouldn't spell the end of the "War on Terror", just like catching a major drug dealer doesn't cause the government to give up the "War on Drugs". The government has declared another war on a vague idea that it uses to justify a wide range of military interventions, and has portrayed the "enemies" as waging an equally ridiculous war on a vague idea (the so-called "War on Freedom"). If they did end up catching Osama, they'd promptly execute him and then turn around and say "see, look at the success we're making in the War on Terror, but the fight isn't over so we need your continued support".