If US implemented very restricted immigration policy in earlier 20th century, mass of European immigrants might start to move to Canada. I would imagine that Canada would implement a similar policy soon.
Imagine 4 million Italian immigrants wanted to come to Canada from 1890 to 1920. Canada's population was 8 million in 1920. I can't imagine Canadian government would welcome 4 million immigrants who barely speak English.
Hypothetically speaking, Canada welcomed these Italian immigrants and most of them were settled in Manitoba and Saskatchewan. These provinces might become another Quebec in 20 years.
I believe US immigration policy has big impact on Canadian ones. I would think immigrant would move to Australia or South America.
There was no way that Canada could accommodate that large a number of Italian immigrants, as the number of jobs available was simply not there. Also, during this period nearly half of all Italians immigrants arriving in the U.S. returned to Italy, one only has to realize that by 1920 there were only 1.6 million Italian born individuals in the United States despite much higher numbers of immigrant arrivals. The vast majority, or around 85% were hailed from what had been the Kingdom of the Two Sicilies and lived in urban areas. They were largely attracted to the factories of the Eastern U.S. and Midwest, American industry thrived prior to 1929. Additionally, before 1913, American industry was protected by what were at that time some of the highest tariffs among Western countries. This policy would not have had so much success had the U.S. not had what at the time was the world's largest internal market. In Canada there were factories, but most industries were branch plants without the massive numbers of work opportunities south of the border. Additionally, the Italians in the U.S. were largely unskilled workers who disproportionately male and were often known as "birds of passage" because they would come and go between Europe and Italy, often more than once. Though Canada had some heavy industry, the steel and automobile industries were still nascent and would grow Southern Ontario, but these do not emerge overnight.
According to the Census of 1921, Canada had 35,531 individuals born in Italy (compared with 1.610.113 in the U.S.), a number that increased to 42,578 by 1931. These numbers were similar to those in Chile, Peru or Mexico, and much lower than those in Argentina, Brazil or Uruguay. The majority of these Italians were concentrated in the urban Ontario and Montreal. With 9,000 Italian-born individuals in Toronto by 1921. However, in 1920 even smaller New England cities such as Providence, New Haven and Hartford all had more than twice as many Italian-born individuals as Toronto, and this is ignoring the 390,825 in New York City or 136,793 in Philadelphia. Canada did attract a large number of Italians after World War II into the 1970s, but at that time Canada had a much more dynamic economy with larger cities and was able to find work for so many Italians. The automotive industry, particularly grew during this period, with automobiles becoming Canada's largest export by the 1960s. If the U.S. remains closed to immigrants, I do not see it being very open to industrial imports, and for Canada's industries to grow access to the U.S. market is necessary.
Prior to World War II Argentina in some ways mirrored Canada. Both countries' economies relied on the export of natural resources and with small but growing industrial sectors. Both had fairly high standards of living and attracted large numbers of immigrants between 1900 and 1914 especially. In both countries, a larger proportion of the population had been born abroad than in the United States. Whereas in 1921, 22% of Canada's of the inhabitants had been born abroad, only 13% of the U.S. population were foreign-born in 1920. In Argentina, the 1914 census showed that 30% of Argentina's inhabitants had also been born abroad. However, unlike in the U.S. both countries attracted nearly three-quarters or more came from two countries. For Canada in 1921, 74% of all individuals born outside of the country hailed from the British Isles and the United States, whereas in Argentina 73% of foreign-born individuals came from Italy and Spain. In the U.S. by 1920 the combined total for the United Kingdom (including Ireland), former Austria-Hungary, former Russian Empire, former German Empire and Italy only totaled 72% of the total foreign-born population.
If anything, without the U.S. as an option Canada would likely attract more Italians, but not likely in the numbers that South America would. Argentina tended to attract a much larger portion of skilled Italian immigrants, particularly as the similarity of the Spanish to Italian dialects offered workers greater opportunities than in the United States for the skilled and semi-skilled. Brazil too, where the Italian-born population had declined from a peak of around 675,000 in 1905 to 558,405 in 1920 due to far fewer arrivals after 1903. With fewer options, Italians I would expect Italian immigration to remain at over 100,000 per year as it was in 1897, whereas by 1910 fewer than 15,000 Italians immigrated. The number of Portuguese and Spanish immigrants to Brazil continued to climb, during this period, so there were economic opportunities. However, it appears that the United States emerged as a more desirable destination for short-term Italian emigrants than Brazil.
For Canada, I can see a larger number of Scandinavians, Poles and Ukrainians, but even IOTL by the 1930s the Prairie provinces experience a negative out migration, particularly to Ontario and Western Canada can only hold so many people. Saskatchewan and to a lesser extent Manitoba experienced a sort of stagnation that was not overcome until the 1950s, and even then their economic opportunities still were far fewer than those offered in other Ontario, Quebec, Alberta and British Columbia. Additionally, one has to remember there was significant emigration from Canada to the United States with 1,138,174 individuals born in Canada and Newfoundland living in the United States by 1920. If the U.S. is closed, these people are going to need to remain in Canada or find opportunities elsewhere. Perhaps with New England and Michigan closed, the French Canadians are encouraged to settled in the Prairies in larger numbers.