Well... Lets say that none of that Finland episode was faked so... I guess
The reason from my point of view is this: When Conan asked those angry letters to be sent there, of course most who follow the show wanted to participate (It was winter, we were bored). Then the whole thing just kept growing and finally he was going to come here. Finns don't have very good self esteem, and when someone as big as Conan (after all pretty known show) comes to Finland because of his interest towards Finland, it is quite flattering to most of us. Conan got big after he mentioned Finland over and over. Before that it was just another talk show. What comes to the precidental campaing... it didn't really count at all. The support was just showing our presidents pic at the late night show 
Oh but one thing about the Finland episode. He only showed the dull side of our country and all the people that was seen there were complete idiots (where did he dig all of them?). So wasn't very good PR work 