I am curious, why attend a non-credentialed school to start with? Why not just attend a credentialed one if that is the ultimate goal?
Some schools (I believe Greenville Seminary is one example) question whether a Christian school should place itself under the oversight of a government accreditation agency. They may very well have a valid point. Some schools do this because they know they will qualify for federal assistance (or, more precises, for their students). But he who pays the piper calls the tune; if you let the gov't in the back door, don't be surprised if one day they begin telling you what you can and can't do.