I don't see there being a problem as the way the law is worded it doesn't specifify that prior experiance be from California. And, the form stating experiance is one of those "under penelty of perjurory, the above is true and correct" type of things. It asks for either an apprenticship certificate, or employer contacts, that they are supposed to check up on. (I don't think they have the man-power to check up on squat, so I would say just fire it away.) The whole point is to pass the test essentially, at this point I really don't think they care who takes it.
And many employers are not asking for certification as of yet, due to a complete lack of knowledge about this law, many don't know it exists, or have no confidence in it going forward.
I would however advise in 1. checking the job market in SD before going there, (a recent post here described a dismal market.) maybe try to land a job before going, and 2. applying for the test before going.
Here's the form: http://www.dir.ca.gov/DAS/ElectricalCertificationForm.pdf