No.

The concept of dodging the draft began with the Civil War in the 1860s. In fact, there is a place in New Brunswick in the Mapleton District in Carleton county referred to as Skedaddle Ridge. It was a place where many Americans had settled after skedaddling across the border from Maine to escape having to fight in the war.

Americans and people in what is now Canada had been crossing each other's borders for years, often to find work or to settle in a new home. But once the Civil War began and Abraham Lincoln became desperate for soldiers to fight for the North, the border crossings took on a different slant. Despite offering money for soldiers to sign up, by 1862 the government enacted legislation that would draft men into the army. It also made a proviso that a citizen could provide a substitute in his place. This was one of the reasons so many Canadians decided to sign up for the war, and there was a brisk trade in soldiers of fortune in border cities such as Buffalo and Detroit.

But some of the American draftees decided to put themselves out of reach of authorities by crossing into Canada, according to the late historian Marcus Lee Hansen. These men were called "skedaddlers." Desertion and draft dodging were especially prevalent in border states such as Maine, New Hampshire, New York, Wisconsin and Minnesota. Because many of these men were experienced farm hands and labor was short in many parts of Canada, they were initially welcomed. They were often glad of the refuge and would work for lower than average pay. By 1864 these skedaddlers were numerous enough (some estimates were as high as 15,000) that people were upset that Canadians had trouble competing for jobs.

When the war ended, many draft dodgers decided to return home to America, and an amnesty proclamation in May, 1865 assured them they wouldn't be punished. Hansen writes that even people who had left the U.S. for Canada before the war caught the spirit of the time and moved back to the country where they'd been born.

Ironically during World War I, it was the U.S. that provided a convenient refuge until 1917 for Canadians who didn't want to enlist to fight overseas.