Yes it did come two piece stock. Small numbers of them may have had one of the two pieces of wood removed by 3rd party (when someone "bubba-ed" it to make it "sporty"). But originally they all resembled something similar to the Enfield battle rifles.
These were trainer rifles during WW2 to teach marksmanship to Airforce and I think Navy recruits...I'm not sure what the Army did, but the Army may have used actual Enfields or Ross Rifle trainers in .22LR for the same purpose. All the ones made for WW2 Canadian military service are stamped with a serial number on the bottom of the wood stock where your hand grip is. Some were issued with a peep sight, some with a more "hunter" style leaf rear sight like most Cooeys normally have.
The wood stocks on the actual trainers sometimes (always???) had a steel bar in the foregrip, to give it weight and ballance closer to a battle rifle like an Enfield. On rare occasions, they mounted a fake "magazine" just in front of the trigger guard...maybe to emulate a C2 LMG? or the Browning BAR? (Not sure if that makes sense...never heard of Canucks issued the BAR, and the C2 would be way after the war).
Postwar they were given to cadet units across the country, and some highschools once deactivated for marching/drill teams. Many were then destroyed. No idea...but I get the feeling well more than half were destroyed. But there are enough still kicking around for the Canadians that want one.
I bought one last month after seeing it at a gunshow and not knowing anything about it asked the owner. It had Redfield target peeps on it...so mine is not totally original. And the wood has a couple of gouges. But...its what I wanted, is Canadian made, Canadian history, WW2 history, a solid rifle sized for an adult, great trigger (well mine does anyway), and only cost me $250. An ALL original with few blemishes can go for closer to $400 - 550 I think.
Single shot, so no magazine. Highly reliable in Canada's harsh outdoors. Prized in America for its superior accuracy, back when these were in production, they were priced 3 times higher than Yankee offerings and still sold very well. In America a great example can go for $600 or more.