Yes, that's how my boyfriend was diagnosed with colon cancer. He was having trouble breathing and was then diagnosed with asthma. But the medicine didn't make him better. Within two weeks after the diagnosis, he was in severe pain and breathing was so difficult he couldn't talk. His lung had collapsed from cancer which had spread from the colon to the lung lining (and he had pneumonia and there was cancer on the liver and phenomenally anemic - and it wasn't diverticulitis that was ailing him earlier). It was scary dire.
Fast forward a couple of months on chemo, there's a small lingering cough, his anemia is nearly all gone, he's able to breath well enough to do 5 min on the treadmill. He gets another scan at the end of this month!