Another issue with unaccredited programs is the quality of the program. In your area, you might know whether the specific unaccredited programs provide good training. If you are applying for an unaccredited program out-of-state, you pretty much throwing a dart at the board. Also, if you plan to eventually move or find a job in a different state, it is so much more helpful to have an accredited program on your CV.
But I do want to mention that in my area, we have a couple of excellent unaccredited programs. Some of them are planning to pursue accreditation, and for some of them their structure does not permit for accreditation (50% of time in hospital and 50% of time in a business environment).