Highway 1CA (coast highway)

Possible, yes. Don't Do It!!!
You will be on the wrong side...drop off cliff side, with little or no shoulder a flimsy guardrail and a vertical drop into the ocean. There are very tight curves...like you can check your own tail-lights. The road is well traveled so you will have cars speeding toward you, light trucks coming at you, and you will probably have a line of cars angrily following you.
It is a beautiful drive. Basecamp in Carmel or Morro Bay and take a day drive in the tow vehicle to enjoy the sights and pull outs. But this is the one area of PCH-1 that I would not drive in an RV. I've done it twice, 10 years apart, going North. Guess my fading memory got the best of me.
Happy Trails.

I would not suggest this! High cliffs with drop offs and no guard rails, no extra space on the sides of the road. You will not get to enjoy the view with the fiver on the back... Just the truck is plenty!

I have a 33ft fifth. I was thinking of driving down CA1 from Monterey thru Big Sur and on to Santa Barbara. Is this possible

Depends on how good of a driver you are. It is very possible but there are a few tight corners and you will need to know where your wheels are both for the fifth and the tow vehicle on the corners.