Legal Question in Immigration Law in California

Generally speaking, the California DMV only will issue ID with demonstration of valid legal authorization to be in the U.S. -- or some other court documentation showing that you are able to be here. So, not sure you will be able to renew the ID. As far as whether you can be arrested, it's highly unlikely that you'd be arrested there. But, note that an arrest could be made, for cause, at most times when out in public.