A little web searching says beginning with the 2015-2016 season, anyone with a deer tag must report their harvest, even if they did not actually go hunting. I thought I would mention it in case you didn't know.
https://www.wildlife.ca.gov/hunting/deer
Somewhere in that same link you will probably find the answer to your question.
Most, if not all states regulations say that a muzzleloading rifle can be used in place of a center-fire rifle during the regular hunts, as long as it meets the requirements for muzzleloaders on the species being hunted.
The laws say that the muzzleloading season is for muzzleloaders only. That's to keep the center-fire guys from hunting during that hunt.
Put a different way, I can use my muzzleloader for deer hunting in Arizona during the muzzleloading season or during the regular high power rifle season. The gun I choose is up to me.
Probably the easiest way to find the answer is to do as Mr. Eames suggested. Call the California Game and Fish department and ask them.