By "traditional law school", I assume you mean ABA approved. My understanding is that the vast majority of ABA schools will not accept credits from a non-ABA school. A few of the ABA schools in California will accept credits from Calbar accredited schools, but not unaccredited schools. Just check the transfer applicant info on each school's site, and it should list their policy.
As far as other criteria (LSAT, etc), transfer applicants still have to meet the normal requirements for admission. This means taking the LSAT, holding a bachelor's degree, registering with LSAC, etc.
It's possible that some of the Calbar accredited schools might accept unaccredited coursework, I'd check with each school individually. No school, however, is required to accept such credits even if their policy allows for it. You'd probably have an uphill battle no matter what.
The bottom line is, don't attend a school you aren't prepared to graduate from. I think this is especially true of unaccredited programs, since transferring will likely be very, very difficult. I would contact each school you're considering and ask if they have ever had a student transfer to an ABA or CBE accredited school. That should give you a good indication.