Citizenship is governed by the Citizenship Act.
http://www.canlii.org/ca/sta/c-29/If you were actually in the Canadian Armed Forces and serving outside Canada, that time would be counted toward the time needed as a permanent resident of Canada before applying for citizenship (s. 5(1.1)), but that's all. And you would have to be a permanent resident (accepted into Canada as an immigrant) first anyhow.
The 1946 Citizenship Act provided that "Immigrants who had served in the Canadian armed forces during the First or the Second World War would qualify for naturalization after only one year."
http://www.cic.gc.ca/english/department/legacy/chap-5.htmlThat is, they had to be accepted as immigrants in any event.
Ah, here we go; the horse's mouth:
http://www.dfait-maeci.gc.ca/canadaeuropa/france/defense/forces-en.aspJoining the Canadian Armed Forces
To enrol in the Canadian Armed Forces an individual must meet the followings prerequisites:
- be a Canadian citizen (see Note 1);
- meet the Canadian Armed Forces medical standard for the desired occupation; and
- meet education level required for the selected military program.
NOTE 1 - Before making an application to obtain a Canadian citizenship <"a Canadian citizenship"?? -- sometimes the language on our bilingual web sites is just appalling>, a person must live in Canada on a permanent basis for three consecutive years. The intention of applying for enrolment into the Canadian Armed Forces does not remove or lessen the required period of permanent residency.
I don't know how that jibes with the Citizenship Act bit about serving in the Forces before becoming a citizen, but I suspect that provision is an anachronism now.
So the short answer is "no" -- no fast track, because no possibility of enrolling (the modern word for "enlisting" hereabouts) if you're not already a citizen.