It depends. The government would rather not have to deal with this and they would have to make special provisions to let these people in. It would be in violation of the US/Canada agreement and an insult to the United States. If this a major influx of refugees the government is going to have choose between Trudeau cultivating the appearance of a humanitarian and the geo-political fallout.
100 million? A billion? A TRILLION?
I am not an immigration lawyer, but if they came to N. America and their first country of arrival was the US, then I would think that they can be handed back to the US authorities.
That said, I am sure that if the US authorities (officers on scene) can sluff off the chore of dealing with these illegal aliens, they will. Let the US and CDN bureaucrats deal with the legal problems. For example, they would wait until their chain issued a directive saying that if the Cdn authorities refused them entry, then the US would have no choice but to take them back and place them under arrest.
The problem here, the way I see it at any rate, is politics gets in the way of a Mountie saying, "Uh, uh! Back you go!"
Have the RCMP received instructions on how to handle the illegal aliens? Has the US border authority received instructions on how to handle any illegals crossing from the US into Canada? (IOW, let 'em go!)
Some of this we will never know. In the meantime, bureaucracy kicks in and what one would think is a simple process, gets bogged down. If after a few days, we see buses full of illegals being sent back to the US, with their wounds bandaged, then I will say the system is working.