It is definitely possible. People ride bicycles from Maine to Georgia during the summer so why would it not be possible for the west coast? I would take the coastal highway and enjoy doing so. A good rule of thumb for bicycles is to plan about 100 miles per day. That is actually not hard to do, 20 mph for 5 hours. 10 mph for 10 hours. So you should plan for a 3 week trip and plan on enjoying yourself.
