They are.
Going back to trying to figure out where the legal aid programs came from, I went to the charter, of course. There is a right to retain and instruct counsel if a person is in custody or under arrest. Other than that, there does not appear to be an actual absolute right, although the courts have given signals that accused and perhaps those in some other contexts might require some representation. In some cases a judge may actually insist on it, presumably foisting that burden on the provincial legal aid plan when that happens.
I don't know how prosecutors respond, but assuming some of that happens and pops up from time to time, I was curious about your reference to the refugee component. As far as I understand it, these individuals would not be residents of Ontario or a particular province. Are they served by duty counsel, or would they actually have the ability to obtain a certificate?