As a Sea Log officer, you are likely to spend your career with the RCN, and some ashore postings to non-Navy units (largely in NDHQ). Postings to the CA and RCAF would be the exception, rather than the rule.
However, functions like supply and finance are "purple" - shared between the three environments (and CMP and SOF and the MPs and...), so managing those systems are officers of all three persuasions.
While theoretically possible, it is extremely unlikely that a naval logistics officer would be posted to an Army or Air Force position. In fact the only real reason a naval logistics officer would be posted to an Army or Air Force position would be for some unique extenuating circumstance (e.g. a compassionate posting). For the most part, naval logistics officers can expect to spend the bulk of their careers in Esquimalt, Halifax and/or Ottawa. There is also the chance of being posted to Borden (where the school is) and/or Kingston (joint HQ). Finally, there are a variety of joint, purple and naval positions outside Canada. While you will probably never see a naval logistics officer in a service battalion, or an army logistics officer in a ship, the same cannot be said for logistics NCMs.