of course they can refuse it, ive been following arc cases for the past 2 years and have only seen 1 get denied, and ive seen at least 10-15 get approved.
but if you provide all the necessary documents, such as the 400$ fee, the letter on reasons why you should be allowed to come back to Canada and pass the security clearance, there is no reason for them to deny you. unless you have a bad background or are a security threat. you still have to satisfy the officer that you will behave in Canada and not repeat whatever made you get deported in the first place.
but out of all the arcs in different categories such as work permits, visitor, skilled worker, family class etc. family class has the highest rate of getting approved because its the Canadian governments goal to keep families together.