In CA, by law, an engine change must retain the emissions equipment on the engine which is being installed. It would be a very difficult, complex and expensive project to transplant an LS3 into a C3, but it could be done. My guess is that most smog check stations, confronted with an LS3 in an 81, are going to send you to a State referee station and once you get there, you'll have no choice but to meet the letter of the law.
In the O.C. the enhanced smog check is required and to pass that would probably require all OE emissions controls on an LS3.
In a practical sense, if you really want to do the Gen 4 V8 into C3 swap, you'd be better to sell the 81 and buy an older car which is exempt from the biennial smog check and use that for the swap.