I highly doubt credits from any private school (or public) will necessarily transfer to a public school or any other school. I took classes at a different State University (Colorado) and have had the run around getting them approved at Sac State and ARC.
Assuring that a school is accredited by the proper accrediting body does not necessarily mean that another school will accept the credits. Sometimes, even classes taken at a State and a UC don't transfer exactly, as each school is free to set their own requirements.
The only guaranteed to transfer classes are those spelled out in a "guaranteed transfer agreements" between community college and State / UC Schools
and classes specified as transferable on "assist.org" These are written, signed agreements between schools to accept certain classes.
That being said, I'm in your area and there are a few other private LVN programs you may want to check out besides CAJ and Curam. Kaplan, Twin Rivers, Yuba's Sutter-One Stop, Unitek and Carrington. In Stockton, there's also Xaviar and one other LVN program, whose name I can't recall off-hand.
One reason I chose not to attend CAJ is because they seem to never know exactly when their next program will start and they have a lot of prereqs. I chose an LVN program that incorporated the necessary classes into the program AND was a short duration.