No there is not mention or evidence to back the two's relation. So they are not related. It just a speculation. France took custody of Canada, though being "father" is just a fanterm.
But France is Italy's big brother. France is also Canada's dad, correct? So wouldn't that make Italy Canada's uncle?
Again, I think most fan speculation on Hetalia family trees will be speculation unless Himaruya specifies otherwise.
IMO, there's no canon backing toward France being Canada's blood-related "father" (although, I prefer to see him as such, regardless)--meaning, if I rephrased your question as "isn't Canada technically related to Italy IN THE SERIES?" I would have to say that Himaruya doesn't seem to have made any remark on the Canadian-Italian relationship, so it's unanswerable by Hetalia Wikia. So far, anyway.
HOWEVER--and I'm just guessing, here--I think you're actually curious about the Canada-Italy relationship IRL? Cue Wikipedia passage:
"The first explorer to North America and to Canada was the Venetian Giovanni Caboto (John Cabot). His voyage to Canada and other parts of the Americas was followed by his son Sebastiano Caboto and Janus Verrazanus (Giovanni da Verrazzano).
During the New France era, France also occupied parts of Northern Italy and there was a significant Italian presence in the French military forces in the colony. Notable were Alphonse de Tonty, who helped establish Detroit, and Henri de Tonti, who journeyed with La Salle in his exploration of the Mississippi River.
Italians made up a small portion of the population, however, and quickly lost their ethnic identities. In 1881, only 1,849 Canadians claimed to be Italian. A number of Italians were imported to work as navvies in the construction of the Canadian Pacific Railway..."
Quick summarization of the rest: Italian communities and identity in Canada were revitalized by the early twentieth century, although Canadian-Italian relations (diplomatically and on an individual scale) were extremely strained during the Great War (for obvious reasons). Immigration from Italy increased (again) after the Second World War, however, although revisions to Canada's immigration policies and the gradual (relative) "prosperity" of Italy eventually slowed emigration to a trickle by the 60's and 70's.
Other key notes might be that Italians identify as the 5th largest ethnic group in Canada as of the most current census--and Canada and Italy currently have fairly close diplomatic and economical relations. (According to the Canadian government, anyway. http://www.canadainternational.gc.ca/italy-italie/bilateral_relations_bilaterales/index.aspx?lang=eng&menu_id=8&menu=L)
So, in conclusion--in other words, linking all this back to Hetalia--one could say that Canada and Italy (especially North Italy) MIGHT have met when they were younger (especially if France and Spain made regular trips to the New World IRL), but they are probably not related by blood, just as Canada isn't related by blood to either Korea or China--he simply hosts a LARGE amount of their foreign exchange students, amongst other ethnic groups.
However, it's probably safe to say that if the Canadian-Italian relationship is ever mentioned by Himaruya (and he's actually been Doing His Research), the two nation-tans will probably be depicted as being marginally close friends, even if Feliciano ends up forgetting most of the time (due to his nature).