The quick answer is "Yes". I have an 89 Civic hatchback and have gotten the B18C installation through all the Referee requirements. (ya, I live in California) Here is what you will be facing;
When you go to register the car they will require you to show a smog certificate unless the prior owner had recently done such (this is only valid for a short amount of time, like a month or two).
When you go to a smog check station, they will notice the swapped engine and tell you that you have to go to a State Referee station to get the installation "certified".
You have to call the state and set up an appointment to take your car in for review.
At the Referee station, they will verify that the engine is the same year as the car, or newer. All smog equipment for the newer engine must be installed and working. It must be USDM specification smog stuff.
If you have an item like an aftermarket exhaust manifold (I've got a DC sport header), it has to have a California CARB certification for it and it has to be for the year of the engine. (the Referee checked on his computer the number that is on my header to be sure)
Once the visual check is done, they do a smog check (on the rollers).
If you pass, they apply on your car a sticker stating that the car is legal and future smog checks should be run as if the car is a GSR. In other words, you never have to go back to the Referee again.
If you were pulled over by the police and they questioned the engine, all you have to do is show them the sticker.
It's not hard to do and feels REAL good once done.
Here is a tip; Act professionally and don't try to "sneak" anything past them! They do this for a living and I'd bet that they have seen just about every trick ever thought of.
Another thing to do is have a "pre-check" done at a standard smog check station. Make it clear with them that you do NOT want it hooked up to the DMV system. By doing this, you will have a feeling that the emissions are within a reasonable range.
Wes Vann