I will defer to Warren's scholarship; undoubtedly he knows more about this than anyone else here.
My own impression is that when the Canadian troops were hurriedly mobilized and sent overseas, most them were issued the Mark III, which by 1913 was Canada’s adopted standard. Before the troops departed, a shortage of rifles led to the addition of some 8,000 Mark II* rifles. In England the CEF then spent some months in training (of which some photos showing Mark IIs have survived).
However, by the time the CEF shipped out to France, the Mark III would likely have been issued uniformly, if for no other reasons than to avoid a logistical nightmare and because the Mark II could not be charger-loaded. Though the Mark II had a patented follower depressor that facilitated “dumping” loose cartridges into the magazine, after the British experience in the Boer War, charger-loading was regarded as well-neigh indispensable. In the absence of any period photographs showing Mark II rifles actually at the front in France, it seems almost certain that the relatively few Mark II*s that went overseas stayed in England.
M