According to George Fox's Student Admissions and Outcome Data, their APA-accredited internship match rate for the last few years is between 5% and 25%, which is pretty abysmal. Not going to an APA accredited internship will seriously limit your options as a psychologist. George Washington's is better (hovers around 75%) but still is not great.
Cannot agree with this enough. And IBR might not be around forever, so banking on that is probably not a good idea.