It's a good idea to start looking into it now before current insurance expires, but I'm not so sure about the existing coverage mattering much. If there are no preexisting conditions, great, but if you do have at least one, I'm pretty sure they can decline you even with existing insurance coverage except in certain circumstances (e.g. cobra).

http://www.mrmib.ca.gov/MRMIB/MRMIP.shtml is worth looking into if you find yourself unable to get health insurance as a result.