Muggle, how much money do you want to spend on building up this CCM? If in the end you wind up buying lots of new parts (new wheels, new cranks, pedals?) it might be easier, only slightly more expensive and certainly less back-yard looking to buy a used track bike or even a.....................

KILO TT

Seriously though, even if you fixify this CCM, it's still a Canadian Tire bike (the running joke growing up was that CCM stands for Canadian Crap Mobile). Do what you like though, it will be an adventure!