Well, Kristin Seaver has argued that the Bristol expeditions to the Grand Banks were more frequent that we've recognized. Because they were kept secret by the families undertaking them. And in fact that they were the last straw for the Norse in Greenland, as the fishermen recruited the young people away.
The problem here is, though that what them losing secrecy would do isn't publish the discovery of America, but publish the discovery of exploitable amounts of fish off the Vinland. An area that was known of, if previously of little interest.
When Colombus returned, he was desperate to show value for his trip, which was financed by the authorities. So he grossly exaggergated the amount of gold he'd found, causing a vawe of interest.
In this case, we'd see a more gradual interest. Fishing nations would be interested, and more ships would start sailing...eventually there'd be sufficient activity to start some support on the shore. Some people would start farming...a lot more gradual than the Colombus Gold Rush Special.