I work at a big4 Accounting firm, and was hired on a post-graduate work permit. It's doable, but don't expect an easy ride. There are some hurdles - for example as a temporary foreign worker, you can't get anything higher than a Reliability Security clearance, which can impact the jobs you can put on. Depending on your country of origin, you may need more travel visas without a Canadian passport, as you're often sent abroad for audits.
CA firm recruitment is highly dependent on the economy, so I wouldn't dare crystal ball into the future on your chances. If you're doing a CA, you have many more options now (you can get a CA through industry these days - doesn't even need to be a CA firm). CA recruitment is largely based on your grades (to get the initial interview), then your ability to make a good impression during the networking and interview stages.
My suggestion to you would be to work on the short term goals first, and be open to things not going to plan. Rules can change, your interests can also change, and the economy can change. Many people finish Accounting majors and decide it's not for them. I'd say for each year we recruit, about 20-25% of new hires quit audit after a year because it isn't for them. There's high attrition in this field, so keep that in mind. Focus on the short term milestones and the things you have control over (your grades, your networking and inter-personal skills), give it your best shot and you can definitely achieve the path to citizenship.