Yes, for a given definition of 'North Pole'.
You see, there are three different 'North Pole's
Geographic North Pole, which is defined as 'the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface' (ignoring precession).
Magnetic North Pole, defined as 'the point on the surface of Earth's Northern Hemisphere at which the planet's magnetic field points vertically downwards'. This is what your compass points at.
Geomagnetic North Pole: the Magnetic North Pole and Magnetic South Pole are not actually directly opposite each other. This is the closest approximation to 'but, what if they actually were?'
As should (hopefully) be pretty obvious, the first definition is completely incompatible with your question: as soon as you move the axis of rotation, the Geographic North Pole moves with it. Canada cannot, by definition, rotate through the Geographic North Pole, and on down to the Geographic South Pole.
However, the Magnetic and Geomagnetic North Poles move. They are also largely independent of the Axis of Rotation. In the 1850s / 1860s, they actually got all the way down to King William Island in Canada - that's a quarter of the way to the equator! And, sometimes, Magnetic North is in the Geographic South.
So, you could (theoretically) have a situation where Magnetic North was pretty much on the equator. Countries could then rotate 'North' (Magnetically) past the Pole, and continue 'South'. However, they are still rotating around the planet's axis: For Magnetic North to be roughly where Geographic North currently is, and Canada to rotate through it, you would need the Geographic North Pole (or the Geographic South Pole) - and the Earth's Axis - to be somewhere around Cape Town
It should be noted, of course, that this would make Canada nice and warm, while Hawaii would be covered in ice.