They usually just show a short recording after the actual ceremony has taken place. Meanwhile, stupid categories like best video and so on are shown live on prime time. I read about it in an article in swedish close-up magazine where Mike said he felt nauseus around all the fake people at the grammy awards. He had hoped to win so he could get up and tell everyone what a bunch of asskissers they where, but then he said that he would probably not have dared. I also think he said that he never wanted to go there again.
This is all from memory so it might not be 100% accurate.
I don't think the band really cares about the award, althought it would probably mean some commercial success in Sweden, like what happened to The Haunted in 2001.